document.write( "Question 204560: X ^ 4 – 2 x ^ 2 = 8\r
\n" ); document.write( "\n" ); document.write( "That is: x to the fourth minus two x squared equals eight.\r
\n" ); document.write( "\n" ); document.write( "Find all solutions for x.\r
\n" ); document.write( "\n" ); document.write( "I have attempted this problem several times and am fighting with it, I thought to take the square root of both sides and that didn't work, and I tried adding eight to both sides but I am still stuck and don't know how to proceed. Please help! \n" ); document.write( "

Algebra.Com's Answer #154410 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve for x:
\n" ); document.write( " $\"x%5E4-2x%5E2+=+8\"$ Subtract 8 from both sides of the equation.
\n" ); document.write( " $\"x%5E4-2x%5E2-8+=+0\"$ Now you can make this look like a quadratic equation by temporarily substituting $\"x%5E2+=+z\"$
\n" ); document.write( " $\"z%5E2-2z-8+=+0\"$ Factor this.
\n" ); document.write( " $\"%28z%2B2%29%28z-4%29+=+0\"$ Apply the zero product rule.
\n" ); document.write( " $\"z%2B2+=+0\"$ or $\"z-4+=+0\"$ which means that...
\n" ); document.write( " $\"z+=+-2\"$ or $\"z+=+4\"$ Re-substitute $\"z+=+x%5E2\"$ to get:
\n" ); document.write( " $\"x%5E2+=+-2\"$ or $\"x%5E2+=+4\"$ so this means that...
\n" ); document.write( " $\"x+=+sqrt%28-2%29\"$ or $\"x+=+-sqrt%28-2%29\"$ or $\"x+=+2\"$ or $\"x+=+-2\"$ \n" ); document.write( "

\n" );