Exercise algebra.equations.quadratic.no-abc

Description
solve a quadratic equation without abc-formula

Derivation

3*x == (4-x)*(1-x)

⇒ algebra.equations.linear.distr-times

3*x == 4-5*x+x^2

⇒ algebra.equations.quadratic.move-left

-x^2+8*x-4 == 0

⇒ algebra.equations.quadratic.scale

x^2-8*x+4 == 0

⇒ algebra.equations.quadratic.prepare-split

x^2-8*x+16 == 12

⇒ algebra.equations.quadratic.left-square

(x-4)^2 == 12

⇒ algebra.equations.coverup.power

x-4 == sqrt 12 or x-4 == -sqrt 12

⇒ algebra.equations.coverup.onevar.minus-left

x == 4+sqrt 12 or x-4 == -sqrt 12

⇒ algebra.equations.coverup.onevar.minus-left

x == 4+sqrt 12 or x == 4-sqrt 12

⇒ algebra.equations.quadratic.simpler-sqrt

x == 4+2*sqrt 3 or x == 4-2*sqrt 3