SOLUTION: Find all real solutions: x^5 + 64x = 0. Show steps please.

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Question 643577: Find all real solutions: x^5 + 64x = 0. Show steps please.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E5%2B64x+=+0
To find the solutions to a polynomial equation like this we factor it. And factoring start with factoring out the greatest common factor, GCF. The GCf here is x:
x%28x%5E4%2B64%29+=+0
As a sum of squares, the second factor will not factor further so we are finished factoring (already).
From the Zero Product Property we know that at least one factor must be zero. So
x+=+0 or x%5E4%2B64+=+0
Subtracting 64 from each side of the second equation we get:
x+=+0 or x%5E4=-64
The second equation has no real solutions. It is not possible to raise a real number to the 4th power and get -64. So the only real solution to your equation come from the first equation:
x = 0.