SOLUTION: If (a) does not equal (b), solve for x in terms of (a) and (b): x^2+ax=-b(a+x)

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Question 72679: If (a) does not equal (b), solve for x in terms of (a) and (b):
x^2+ax=-b(a+x)
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
If (a) does not equal (b), solve for x in terms of (a) and (b):
x%5E2%2Bax=-b%28a%2Bx%29 get rid of parens
x%5E2%2Bax=-ab-bx add ab and bx to both sides
x%5E2%2Bax%2Bbx%2Bab=0 rearrange into standard form for a quadratic eq.
x%5E2%2B%28a%2Bb%29x%2Bab=0 This is a quadratic equation in standard form where"
A=1
B=%28a%2Bb%29
C=ab
By inspection, we can see that the equation can be factored because the B coefficient is the sum of the product of the C coefficient. This is always the case, when A=1. So we have:
%28x%2Ba%29%28x%2Bb%29=0
x%2Ba=0
x=-a
and
x%2Bb=0
x=-b

CK
x%5E2%2Bax=-b%28a%2Bx%29
a%5E2-a%5E2=-ab%2Bab
0=0
and
b%5E2-ab=-ab%2Bb%5E2 or
b%5E2-ab=b%5E2-ab


Hope this helps-------------------ptaylor