Exercise algebra.equations.quadratic.no-abc
Description
solve a quadratic equation without abc-formula
Derivation
![](http://ideas.cs.uu.nl/images/external.png)
6 == 4*x^2+4*x+1
⇒ algebra.equations.linear.flip4*x^2+4*x+1 == 6
⇒ algebra.equations.quadratic.move-left4*x^2+4*x-5 == 0
⇒ algebra.equations.quadratic.scalex^2+x-5/4 == 0
⇒ algebra.equations.quadratic.prepare-splitx^2+x+1/4 == 3/2
⇒ algebra.equations.quadratic.left-square(x+1/2)^2 == 3/2
⇒ algebra.equations.coverup.powerx+1/2 == sqrt (3/2) or x+1/2 == -sqrt (3/2)
⇒ algebra.equations.coverup.onevar.plusx == -1/2+sqrt (3/2) or x+1/2 == -sqrt (3/2)
⇒ algebra.equations.coverup.onevar.plusx == -1/2+sqrt (3/2) or x == -1/2-sqrt (3/2)
⇒ algebra.equations.quadratic.simpler-sqrtx == -1/2+1/2*sqrt 6 or x == -1/2-1/2*sqrt 6