Exercise

Exercise algebra.equations.quadratic.no-abc

Description
solve a quadratic equation without abc-formula

Rules for algebra.equations.quadratic.no-abc

Rule name	Args	Used	Siblings	Rewrite rule
`algebra.equations.coverup.negate`	0	yes
`algebra.equations.coverup.numerator`	0	yes
`algebra.equations.coverup.onevar.minus-left`	0	yes
`algebra.equations.coverup.onevar.minus-right`	0	yes
`algebra.equations.coverup.onevar.plus`	0	yes
`algebra.equations.coverup.power`	0	yes
`algebra.equations.coverup.times`	0	yes
`algebra.equations.linear.distr-times`	0	yes
`algebra.equations.linear.flip`	0	yes		a = b ⇒ b = a
`algebra.equations.linear.merge`	0	yes
`algebra.equations.quadratic.abc`	0	yes
`algebra.equations.quadratic.approx`	0	yes
`algebra.equations.quadratic.cancel`	0	yes
`algebra.equations.quadratic.common-factor`	0	yes
`algebra.equations.quadratic.distr-div`	0	yes
`algebra.equations.quadratic.distr-square`	0	yes		(a+b)^2 ⇒ ((a^2)+((2·a)·b))+(b^2) (a-b)^2 ⇒ ((a^2)-((2·a)·b))+(b^2) (a+b)·(a-b) ⇒ (a^2)-(b^2) (a-b)·(a+b) ⇒ (a^2)-(b^2)
`algebra.equations.quadratic.left-square`	0	yes
`algebra.equations.quadratic.move-left`	0	yes
`algebra.equations.quadratic.nice-factors`	0	yes
`algebra.equations.quadratic.no-lin`	0	yes
`algebra.equations.quadratic.prepare-split`	0	yes
`algebra.equations.quadratic.product-zero`	0	yes
`algebra.equations.quadratic.same-con-factor`	0	yes
`algebra.equations.quadratic.same-factor`	0	yes
`algebra.equations.quadratic.scale`	0	yes
`algebra.equations.quadratic.simpler-poly`	0	yes
`algebra.equations.quadratic.simpler-sqrt`	0	yes
`algebra.equations.quadratic.square-both`	0	yes		(a^2) = (b^2) ⇒ (a = b) ∨ (a = (-b))

Buggy rules for algebra.equations.quadratic.no-abc

Rule name	Args	Used	Siblings	Rewrite rule
`algebra.equations.buggy.abc.minus-4ac`	0	no	algebra.equations.quadratic.abc
`algebra.equations.buggy.abc.minus-b`	0	no	algebra.equations.quadratic.abc
`algebra.equations.buggy.abc.one-solution`	0	no	algebra.equations.quadratic.abc
`algebra.equations.buggy.abc.two-a`	0	no	algebra.equations.quadratic.abc
`algebra.equations.buggy.cancel-minus`	0	no
`algebra.equations.buggy.coverup.even-power`	0	no	algebra.equations.coverup.power
`algebra.equations.buggy.coverup.even-power-forget`	0	no	algebra.equations.coverup.power
`algebra.equations.buggy.coverup.even-power-too-early`	0	no	algebra.equations.coverup.power
`algebra.equations.buggy.coverup.square-minus`	0	no
`algebra.equations.buggy.coverup.times-mul`	0	no	algebra.equations.coverup.times
`algebra.equations.buggy.coverup.times-with-plus`	0	no
`algebra.equations.buggy.distr-square`	0	no	algebra.equations.quadratic.distr-square	(a+b)^2 ⇏ (a^2)+(b^2) (a-b)^2 ⇏ (a^2)-(b^2) (a-b)^2 ⇏ (a^2)+(b^2)
`algebra.equations.buggy.distr-square-forget`	0	no	algebra.equations.quadratic.distr-square	(a+b)^2 ⇏ (a^2)+b (a+b)^2 ⇏ a+(b^2) (a-b)^2 ⇏ (a^2)-b (a-b)^2 ⇏ a-(b^2)
`algebra.equations.buggy.distr-times-denom`	0	no	algebra.equations.linear.distr-times
`algebra.equations.buggy.distr-times-plus`	0	no	algebra.equations.linear.distr-times
`algebra.equations.buggy.distr-times-plus-forget`	0	no	algebra.equations.linear.distr-times
`algebra.equations.buggy.distr-times-plus-sign`	0	no	algebra.equations.linear.distr-times
`algebra.equations.buggy.distr-times-too-many`	0	no	algebra.equations.linear.distr-times
`algebra.equations.buggy.divide-negate`	0	no
`algebra.equations.buggy.divide-numdenom`	0	no
`algebra.equations.buggy.division-by-var-both`	0	no
`algebra.equations.buggy.division-by-var-zero`	0	no
`algebra.equations.buggy.flip-negate-one-side`	0	no	algebra.equations.linear.flip
`algebra.equations.buggy.minus-minus`	0	no
`algebra.equations.buggy.multiply-forget-one`	0	no
`algebra.equations.buggy.multiply-one-side`	0	no
`algebra.equations.buggy.negate-all`	0	no
`algebra.equations.buggy.negate-one-side`	0	no
`algebra.equations.buggy.plus`	0	no
`algebra.equations.buggy.priority-times`	0	no
`algebra.equations.buggy.square-multiplication`	0	no		(a·b)^2 ⇏ a·(b^2) (a·b)^2 ⇏ (a^2)·b a·(b^2) ⇏ (a·b)^2 (a^2)·b ⇏ (a·b)^2