document.write( "Question 1013108: Solve x^4 +4x^2 = 32. Find 4 roots. \r
\n" ); document.write( "\n" ); document.write( "Thanks. \n" ); document.write( "

Algebra.Com's Answer #629269 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+z+=+x%5E2+\"$
\n" ); document.write( "Substitute $\"+z+\"$ in the equation
\n" ); document.write( " $\"+z%5E2+%2B+4z+=+32+\"$
\n" ); document.write( "Complete the square:
\n" ); document.write( " $\"+z%5E2+%2B+4z+%2B+%28+4%2F2+%29%5E2+=+32+%2B+%28+4%2F2+%29%5E2+\"$
\n" ); document.write( " $\"+z%5E2+%2B+4z+%2B+4+=+32+%2B+4+\"$
\n" ); document.write( " $\"+%28+z%2B+2+%29%5E2+=+6%5E2+\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"+z+%2B+2+=+6+\"$
\n" ); document.write( " $\"+z+=+4%0D%0Aand+also%0D%0A%7B%7B%7Bz+%2B+2+=+-6+\"$
\n" ); document.write( " $\"+z+=+-8+\"$
\n" ); document.write( "-----------------
\n" ); document.write( " $\"+x%5E2+=+z+\"$
\n" ); document.write( " $\"+x%5E2+=+4+\"$
\n" ); document.write( " $\"+x+=+2+\"$
\n" ); document.write( " $\"+x+=+-2+\"$
\n" ); document.write( "-------------
\n" ); document.write( " $\"+x%5E2+=+-8+\"$
\n" ); document.write( " $\"+x+=+sqrt%28-8%29+\"$
\n" ); document.write( " $\"+x+=+2%2Asqrt%282%29%2Ai+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+x+=+-sqrt%28-8%29+\"$
\n" ); document.write( " $\"+x+=+-2%2Asqrt%282%29%2Ai+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "The 4 roots are:
\n" ); document.write( " $\"+x+=+2+\"$
\n" ); document.write( " $\"+x+=+-2+\"$
\n" ); document.write( " $\"+x+=+2%2Asqrt%282%29%2Ai+\"$
\n" ); document.write( " $\"+x+=+-2%2Asqrt%282%29%2Ai+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "You can plug these back into the
\n" ); document.write( "equation to check \n" ); document.write( "

\n" );