SOLUTION: |x^2+6x|=3x+18 I'm actually a college student trying to help my foreign exchange student with her high school algebra homework. Alas, I have forgotten how to work problems with

Algebra ->  Absolute-value -> SOLUTION: |x^2+6x|=3x+18 I'm actually a college student trying to help my foreign exchange student with her high school algebra homework. Alas, I have forgotten how to work problems with      Log On


   

Question 502207: |x^2+6x|=3x+18
I'm actually a college student trying to help my foreign exchange student with her high school algebra homework. Alas, I have forgotten how to work problems with absolute values. Any help would be wonderful!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
abs%28x%5E2%2B6x%29+=+3x%2B18 Remove the absolute-value bars from the left side and you get two equations thus:
1) x%5E2%2B6x+=+3x%2B18 or 2) x%5E2%2B6x+=+-%283x%2B18%29 Now solve each of these equations for x.
1) x%5E2%2B6x+=+3x%2B18 Rewrite as a quadratic equation in standard form:
x%5E2%2B3x-18+=+0 Factor this quadratic equation.
%28x-3%29%28x%2B6%29+=+6 Apply the "zero product" rule:
x-3+=+0 or x%2B6+=+0 so that...
highlight%28x+=+3%29 or highlight%28x+=+-6%29
2) x%5E2%2B6x+=+-%283x%2B18%29 Simplify the right side.
x%5E2%2B6x+=+-3x-18 Rewrite as a quadratic equation in standard form:
x%5E2%2B9x%2B18+=+0 Factor this quadratic equation.
%28x%2B3%29%28x%2B6%29+=+0 Apply the "zero product" rule:
x%2B3+=+0 or x%2B6+=+0 so that...
highlight%28x+=+-3%29 or highlight%28x+=+-6%29