SOLUTION: Solve for x :(x+1)exponent2+3x(x+1)exponent2+3xexponent2(x+1)+x exponent3 =0

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Question 1100949: Solve for x :(x+1)exponent2+3x(x+1)exponent2+3xexponent2(x+1)+x exponent3 =0
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!

I very much suspect that the equation is supposed to have the first term to the power 3 instead of 2.

As you show the problem, it is not very interesting, or very educational.

But if the first exponent is 3, then there is something to learn from the problem.

So I will answer the question, assuming a power of 3 on the first term.

The equation is then

%28x%2B1%29%5E3+%2B+3x%28x%2B1%29%5E2+%2B+3x%5E2%28x%2B1%29+%2B+x%5E3

The expression is in the form of

a%5E3+%2B+3a%5E2b+%2B+3ab%5E2+%2B+b%5E3 which is equal to %28a%2Bb%29%5E3

So the equation is equivalent to

%28%28x%2B1%29%2Bx%29%5E3+=+0
%282x%2B1%29%5E3+=+0
2x%2B1+=+0
x+=+-1%2F2

The equation has a triple root at x = -1/2.