document.write( "Question 192032: I have never tried one like this can someone help me. the equation is 15x^4-13x^2+2=0 \n" ); document.write( "

Algebra.Com's Answer #144100 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve for x:
\n" ); document.write( " $\"15x%5E4-13x%5E2%2B2+=+0\"$ Temporarily, let $\"y+=+x%5E2\"$ so that $\"y%5E2+=+x%5E4\"$ . Make these substitutions.
\n" ); document.write( " $\"15y%5E2-13y%2B2+=+0\"$ Factor.
\n" ); document.write( " $\"%283y-2%29%285y-1%29+=+0\"$ Apply the zero product rule.
\n" ); document.write( " $\"3y-2+=+0\"$ or $\"5y-1+=+0\"$
\n" ); document.write( " $\"3y-2+=+0\"$ Add 2 to both sides.
\n" ); document.write( " $\"3y+=+2\"$ Divide both sides by 3.
\n" ); document.write( "1) $\"y+=+2%2F3\"$
\n" ); document.write( " $\"5y-1+=+0\"$ Add 1 to both sides.
\n" ); document.write( " $\"5y+=+1\"$ Divide both sides by 5.
\n" ); document.write( "2) $\"y+=+1%2F5\"$
\n" ); document.write( "Now substitute back $\"y+=+x%5E2\"$ in both solutions.
\n" ); document.write( " $\"x%5E2+=+2%2F3\"$ and $\"x%5E2+=+1%2F5\"$ Take the square root in both cases.
\n" ); document.write( " $\"x+=+0%2B-sqrt%282%2F3%29\"$ and $\"x+=+0%2B-sqrt%281%2F5%29\"$
\n" ); document.write( "The four solutions are:
\n" ); document.write( " $\"x+=+sqrt%282%2F3%29\"$
\n" ); document.write( " $\"x+=+-sqrt%282%2F3%29\"$
\n" ); document.write( " $\"x+=+sqrt%281%2F5%29\"$
\n" ); document.write( " $\"x+=+-sqrt%281%2F5%29\"$ \n" ); document.write( "

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