Solving a quadratic - like equation... I am totally confused! Here is the problem: (x^2 + 4x)^2 - (x^2 + 4x) - 20=0. It says let A = X^2 + 4x, then A^2 - A - 20 =0. Then they factored it (A-5)(A+4) = 0 I understand how they factor it, but I do not understand how they got from step one to step two. Someone help me? Where did the A^2 - A - 20 = 0 come from?

Question

Solving a quadratic - like equation... I am totally confused! Here is the problem: (x^2 + 4x)^2 - (x^2 + 4x) - 20=0.    It says let A = X^2 + 4x, then A^2 - A - 20 =0.   Then they factored it (A-5)(A+4) = 0   I understand how they factor it, but I do not understand how they got from step one to step two. Someone help me? Where did the A^2 - A - 20 = 0 come from?

hero · Answer

(x^2 + 4x)^2 - (x^2 + 4x) - 20=0
(       A    )^2 - (      A      ) - 20=0

hero · Answer

A^2 - A - 20 = 0

anonymous · Answer

Well, when you take
(x^2 +4x)=A
You do see that the question is
(x^2 + 4x)^2 - (x^2 + 4x) - 20 =0 right?
So just replace (x^2 +4x) with A, we get
A^2 - A +20 =0
Then factorize it, as (A+4)(A-5) = 0 and you're all set. :)

hero · Answer

Anywhere you see x^2 + 4x, replace it with A

anonymous · Answer

oooooh duh!! Ok, that totally helps now. I don't know why I wasn't seeing that before.

hero · Answer

:D

anonymous · Answer

thank you, that cleared up so much confusion and frustration!

hero · Answer

yw

:D