SOLUTION: I have to solve the equation by factoring first and then applying the zero product principle. so, can someone help me solve x^3 +x^2-7x=7. any help would be appreciated.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have to solve the equation by factoring first and then applying the zero product principle. so, can someone help me solve x^3 +x^2-7x=7. any help would be appreciated.      Log On


   

Question 112057: I have to solve the equation by factoring first and then applying the zero product principle. so, can someone help me solve x^3 +x^2-7x=7. any help would be appreciated.
Found 2 solutions by Earlsdon, stanbon:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
x%5E3%2Bx%5E2-7x+=+7 Subtract 7 from both sides.
x%5E3%2Bx%5E2-7x-7=+0 Factor by grouping.
%28x%5E3%2Bx%5E2%29+-+%287x%2B7%29+=+0 Factor x%5E2 from the first group and 7 from the second group.
x%5E2%28x%2B1%29+-+7%28x%2B1%29=+0 Now factor the common factor of %28x%2B1%29
%28x%2B1%29%28x%5E2-7%29+=+0 Now apply the zero products principle.
x%2B1+=+0 or x%5E2-7+=+0
If x%2B1+=+0 then x+=+-1
if x%5E2-7+=+0 then x%5E2+=+7 so x+=+sqrt%287%29 or x+=+-sqrt%287%29
The three roots are:
x+=+-1
x+=+sqrt%287%29
x+=+-sqrt%287%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve x^3 +x^2-7x=7
x^3+x^2-7x-7=0
x(x+1)-7(x+1)=0
(x+1)(x-7)=0
x = -1 or x=7
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Cheerd,
Stan H.