Exercise algebra.inequalities.quadratic

Description
solve a quadratic inequation

Strategy

<label name="quadraticinequality">
  <orelse>
    <rule name="algebra.inequalities.trivial"/>
    <sequence>
      <orelse>
        <rule name="algebra.inequalities.to-equation"/>
        <succeed/>
      </orelse>
      <label name="quadraticequationstrategy">
        <let>
          <decl var="4">
            <orelse>
              <sequence>
                <orelse>
                  <let>
                    <decl var="1">
                      <choice>
                        <label name="generalform">
                          <choice>
                            <rule name="algebra.equations.quadratic.common-factor"/>
                            <rule name="algebra.equations.quadratic.no-lin"/>
                            <rule name="algebra.equations.quadratic.simpler-poly"/>
                            <rule name="algebra.equations.quadratic.scale" removed="true"/>
                            <rule name="algebra.equations.quadratic.nice-factors"/>
                            <rule name="algebra.equations.coverup.power"/>
                          </choice>
                        </label>
                        <label name="abcform">
                          <rule name="algebra.equations.quadratic.abc"/>
                        </label>
                        <sequence>
                          <rule name="navigator.down"/>
                          <succeed/>
                          <let>
                            <decl var="2">
                              <choice>
                                <var var="1"/>
                                <sequence>
                                  <rule name="navigator.right"/>
                                  <succeed/>
                                  <var var="2"/>
                                </sequence>
                              </choice>
                            </decl>
                            <var var="2"/>
                          </let>
                          <orelse>
                            <rule name="navigator.up"/>
                            <succeed/>
                          </orelse>
                        </sequence>
                      </choice>
                    </decl>
                    <var var="1"/>
                  </let>
                  <let>
                    <decl var="1">
                      <choice>
                        <label name="zeroform">
                          <rule name="algebra.equations.quadratic.product-zero"/>
                        </label>
                        <sequence>
                          <rule name="navigator.down"/>
                          <succeed/>
                          <let>
                            <decl var="2">
                              <choice>
                                <var var="1"/>
                                <sequence>
                                  <rule name="navigator.right"/>
                                  <succeed/>
                                  <var var="2"/>
                                </sequence>
                              </choice>
                            </decl>
                            <var var="2"/>
                          </let>
                          <orelse>
                            <rule name="navigator.up"/>
                            <succeed/>
                          </orelse>
                        </sequence>
                      </choice>
                    </decl>
                    <var var="1"/>
                  </let>
                  <let>
                    <decl var="1">
                      <choice>
                        <label name="constantform">
                          <choice>
                            <rule name="algebra.equations.coverup.onevar.plus"/>
                            <rule name="algebra.equations.coverup.onevar.minus-left"/>
                            <rule name="algebra.equations.coverup.onevar.minus-right"/>
                            <rule name="algebra.equations.coverup.times"/>
                            <rule name="algebra.equations.coverup.negate"/>
                            <rule name="algebra.equations.coverup.numerator"/>
                            <rule name="algebra.equations.quadratic.square-both"/>
                            <rule name="algebra.equations.quadratic.left-square"/>
                          </choice>
                        </label>
                        <sequence>
                          <rule name="navigator.down"/>
                          <succeed/>
                          <let>
                            <decl var="2">
                              <choice>
                                <var var="1"/>
                                <sequence>
                                  <rule name="navigator.right"/>
                                  <succeed/>
                                  <var var="2"/>
                                </sequence>
                              </choice>
                            </decl>
                            <var var="2"/>
                          </let>
                          <orelse>
                            <rule name="navigator.up"/>
                            <succeed/>
                          </orelse>
                        </sequence>
                      </choice>
                    </decl>
                    <var var="1"/>
                  </let>
                  <choice>
                    <label name="squarerootsimplification">
                      <rule name="algebra.equations.quadratic.simpler-sqrt"/>
                    </label>
                    <label name="approximateresult" removed="true">
                      <label name="algebra.equations.quadratic.approx" collapsed="true">
                        <sequence>
                          <let>
                            <decl var="1">
                              <choice>
                                <rule name="algebra.equations.quadratic.approx"/>
                                <sequence>
                                  <rule name="navigator.down"/>
                                  <succeed/>
                                  <let>
                                    <decl var="2">
                                      <choice>
                                        <var var="1"/>
                                        <sequence>
                                          <rule name="navigator.right"/>
                                          <succeed/>
                                          <var var="2"/>
                                        </sequence>
                                      </choice>
                                    </decl>
                                    <var var="2"/>
                                  </let>
                                  <orelse>
                                    <rule name="navigator.up"/>
                                    <succeed/>
                                  </orelse>
                                </sequence>
                              </choice>
                            </decl>
                            <var var="1"/>
                          </let>
                          <let>
                            <decl var="3">
                              <orelse>
                                <sequence>
                                  <let>
                                    <decl var="1">
                                      <choice>
                                        <rule name="algebra.equations.quadratic.approx"/>
                                        <sequence>
                                          <rule name="navigator.down"/>
                                          <succeed/>
                                          <let>
                                            <decl var="2">
                                              <choice>
                                                <var var="1"/>
                                                <sequence>
                                                  <rule name="navigator.right"/>
                                                  <succeed/>
                                                  <var var="2"/>
                                                </sequence>
                                              </choice>
                                            </decl>
                                            <var var="2"/>
                                          </let>
                                          <orelse>
                                            <rule name="navigator.up"/>
                                            <succeed/>
                                          </orelse>
                                        </sequence>
                                      </choice>
                                    </decl>
                                    <var var="1"/>
                                  </let>
                                  <var var="3"/>
                                </sequence>
                                <succeed/>
                              </orelse>
                            </decl>
                            <var var="3"/>
                          </let>
                        </sequence>
                      </label>
                    </label>
                  </choice>
                  <label name="topform">
                    <orelse>
                      <let>
                        <decl var="1">
                          <choice>
                            <rule name="algebra.equations.quadratic.cancel"/>
                            <rule name="algebra.equations.quadratic.same-factor"/>
                            <sequence>
                              <rule name="navigator.down"/>
                              <succeed/>
                              <let>
                                <decl var="2">
                                  <choice>
                                    <var var="1"/>
                                    <sequence>
                                      <rule name="navigator.right"/>
                                      <succeed/>
                                      <var var="2"/>
                                    </sequence>
                                  </choice>
                                </decl>
                                <var var="2"/>
                              </let>
                              <orelse>
                                <rule name="navigator.up"/>
                                <succeed/>
                              </orelse>
                            </sequence>
                          </choice>
                        </decl>
                        <var var="1"/>
                      </let>
                      <choice>
                        <let>
                          <decl var="1">
                            <choice>
                              <rule name="algebra.equations.quadratic.same-con-factor"/>
                              <sequence>
                                <rule name="navigator.down"/>
                                <succeed/>
                                <let>
                                  <decl var="2">
                                    <choice>
                                      <var var="1"/>
                                      <sequence>
                                        <rule name="navigator.right"/>
                                        <succeed/>
                                        <var var="2"/>
                                      </sequence>
                                    </choice>
                                  </decl>
                                  <var var="2"/>
                                </let>
                                <orelse>
                                  <rule name="navigator.up"/>
                                  <succeed/>
                                </orelse>
                              </sequence>
                            </choice>
                          </decl>
                          <var var="1"/>
                        </let>
                        <label name="algebra.equations.linear.merge" collapsed="true">
                          <sequence>
                            <let>
                              <decl var="1">
                                <choice>
                                  <rule name="algebra.equations.linear.merge"/>
                                  <sequence>
                                    <rule name="navigator.down"/>
                                    <succeed/>
                                    <let>
                                      <decl var="2">
                                        <choice>
                                          <var var="1"/>
                                          <sequence>
                                            <rule name="navigator.right"/>
                                            <succeed/>
                                            <var var="2"/>
                                          </sequence>
                                        </choice>
                                      </decl>
                                      <var var="2"/>
                                    </let>
                                    <orelse>
                                      <rule name="navigator.up"/>
                                      <succeed/>
                                    </orelse>
                                  </sequence>
                                </choice>
                              </decl>
                              <var var="1"/>
                            </let>
                            <let>
                              <decl var="3">
                                <orelse>
                                  <sequence>
                                    <let>
                                      <decl var="1">
                                        <choice>
                                          <rule name="algebra.equations.linear.merge"/>
                                          <sequence>
                                            <rule name="navigator.down"/>
                                            <succeed/>
                                            <let>
                                              <decl var="2">
                                                <choice>
                                                  <var var="1"/>
                                                  <sequence>
                                                    <rule name="navigator.right"/>
                                                    <succeed/>
                                                    <var var="2"/>
                                                  </sequence>
                                                </choice>
                                              </decl>
                                              <var var="2"/>
                                            </let>
                                            <orelse>
                                              <rule name="navigator.up"/>
                                              <succeed/>
                                            </orelse>
                                          </sequence>
                                        </choice>
                                      </decl>
                                      <var var="1"/>
                                    </let>
                                    <var var="3"/>
                                  </sequence>
                                  <succeed/>
                                </orelse>
                              </decl>
                              <var var="3"/>
                            </let>
                          </sequence>
                        </label>
                        <let>
                          <decl var="1">
                            <choice>
                              <rule name="algebra.equations.quadratic.distr-square"/>
                              <sequence>
                                <rule name="navigator.down"/>
                                <succeed/>
                                <let>
                                  <decl var="2">
                                    <choice>
                                      <var var="1"/>
                                      <sequence>
                                        <rule name="navigator.right"/>
                                        <succeed/>
                                        <var var="2"/>
                                      </sequence>
                                    </choice>
                                  </decl>
                                  <var var="2"/>
                                </let>
                                <orelse>
                                  <rule name="navigator.up"/>
                                  <succeed/>
                                </orelse>
                              </sequence>
                            </choice>
                          </decl>
                          <var var="1"/>
                        </let>
                        <label name="algebra.equations.linear.distr-times" collapsed="true">
                          <sequence>
                            <let>
                              <decl var="1">
                                <orelse>
                                  <rule name="algebra.equations.linear.distr-times"/>
                                  <sequence>
                                    <rule name="navigator.down"/>
                                    <succeed/>
                                    <let>
                                      <decl var="2">
                                        <choice>
                                          <var var="1"/>
                                          <sequence>
                                            <rule name="navigator.right"/>
                                            <succeed/>
                                            <var var="2"/>
                                          </sequence>
                                        </choice>
                                      </decl>
                                      <var var="2"/>
                                    </let>
                                    <orelse>
                                      <rule name="navigator.up"/>
                                      <succeed/>
                                    </orelse>
                                  </sequence>
                                </orelse>
                              </decl>
                              <var var="1"/>
                            </let>
                            <let>
                              <decl var="3">
                                <orelse>
                                  <sequence>
                                    <let>
                                      <decl var="1">
                                        <orelse>
                                          <rule name="algebra.equations.linear.distr-times"/>
                                          <sequence>
                                            <rule name="navigator.down"/>
                                            <succeed/>
                                            <let>
                                              <decl var="2">
                                                <choice>
                                                  <var var="1"/>
                                                  <sequence>
                                                    <rule name="navigator.right"/>
                                                    <succeed/>
                                                    <var var="2"/>
                                                  </sequence>
                                                </choice>
                                              </decl>
                                              <var var="2"/>
                                            </let>
                                            <orelse>
                                              <rule name="navigator.up"/>
                                              <succeed/>
                                            </orelse>
                                          </sequence>
                                        </orelse>
                                      </decl>
                                      <var var="1"/>
                                    </let>
                                    <var var="3"/>
                                  </sequence>
                                  <succeed/>
                                </orelse>
                              </decl>
                              <var var="3"/>
                            </let>
                          </sequence>
                        </label>
                        <rule name="algebra.equations.quadratic.distr-div"/>
                        <let>
                          <decl var="1">
                            <choice>
                              <sequence>
                                <rule name="check"/>
                                <rule name="algebra.equations.linear.flip"/>
                              </sequence>
                              <sequence>
                                <rule name="navigator.down"/>
                                <succeed/>
                                <let>
                                  <decl var="2">
                                    <choice>
                                      <var var="1"/>
                                      <sequence>
                                        <rule name="navigator.right"/>
                                        <succeed/>
                                        <var var="2"/>
                                      </sequence>
                                    </choice>
                                  </decl>
                                  <var var="2"/>
                                </let>
                                <orelse>
                                  <rule name="navigator.up"/>
                                  <succeed/>
                                </orelse>
                              </sequence>
                            </choice>
                          </decl>
                          <var var="1"/>
                        </let>
                      </choice>
                      <let>
                        <decl var="1">
                          <choice>
                            <rule name="algebra.equations.quadratic.move-left"/>
                            <rule name="algebra.equations.quadratic.prepare-split" removed="true"/>
                            <sequence>
                              <rule name="navigator.down"/>
                              <succeed/>
                              <let>
                                <decl var="2">
                                  <choice>
                                    <var var="1"/>
                                    <sequence>
                                      <rule name="navigator.right"/>
                                      <succeed/>
                                      <var var="2"/>
                                    </sequence>
                                  </choice>
                                </decl>
                                <var var="2"/>
                              </let>
                              <orelse>
                                <rule name="navigator.up"/>
                                <succeed/>
                              </orelse>
                            </sequence>
                          </choice>
                        </decl>
                        <var var="1"/>
                      </let>
                    </orelse>
                  </label>
                </orelse>
                <var var="4"/>
              </sequence>
              <succeed/>
            </orelse>
          </decl>
          <var var="4"/>
        </let>
      </label>
      <rule name="algebra.inequalities.give-solution"/>
    </sequence>
  </orelse>
</label>

Locations