Exercise algebra.equations.quadratic.no-abc
Description
solve a quadratic equation without abc-formula
Derivation
-x^2-2*x+2*x^2-7 == 0
⇒ algebra.equations.linear.mergex^2-2*x-7 == 0
⇒ algebra.equations.quadratic.prepare-splitx^2-2*x+1 == 8
⇒ algebra.equations.quadratic.left-square(x-1)^2 == 8
⇒ algebra.equations.coverup.powerx-1 == sqrt 8 or x-1 == -sqrt 8
⇒ algebra.equations.coverup.onevar.minus-leftx == 1+sqrt 8 or x-1 == -sqrt 8
⇒ algebra.equations.coverup.onevar.minus-leftx == 1+sqrt 8 or x == 1-sqrt 8
⇒ algebra.equations.quadratic.simpler-sqrtx == 1+2*sqrt 2 or x == 1-2*sqrt 2