document.write( "Question 643577: Find all real solutions: x^5 + 64x = 0. Show steps please. \n" ); document.write( "

Algebra.Com's Answer #404555 by jsmallt9(3758) $\"\"$ $\"About$

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$\"x%5E5%2B64x+=+0\"$
\n" ); document.write( "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:
\n" ); document.write( " $\"x%28x%5E4%2B64%29+=+0\"$
\n" ); document.write( "As a sum of squares, the second factor will not factor further so we are finished factoring (already).
\n" ); document.write( "From the Zero Product Property we know that at least one factor must be zero. So
\n" ); document.write( " $\"x+=+0\"$ or $\"x%5E4%2B64+=+0\"$
\n" ); document.write( "Subtracting 64 from each side of the second equation we get:
\n" ); document.write( " $\"x+=+0\"$ or $\"x%5E4=-64\"$
\n" ); document.write( "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:
\n" ); document.write( "x = 0. \n" ); document.write( "

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