document.write( "Question 1038065: What are real or imaginary solutions of the polynomials. x^4-52x^2+576=0. \n" ); document.write( "
Algebra.Com's Answer #652780 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Let \"+z+=+x%5E2+\"
\n" ); document.write( "then \"+x%5E4+=+z%5E2+\"
\n" ); document.write( "-------------------
\n" ); document.write( "Rewrite the equation:
\n" ); document.write( "\"+z%5E2+-+52z+%2B+576+=+0+\"
\n" ); document.write( "Complete the square:
\n" ); document.write( "\"+z%5E2+-+52z+%2B+%28+52%2F2+%29%5E2+=+%28+52%2F2+%29%5E2+-+576+\"
\n" ); document.write( "\"+z%5E2+-+52z+%2B+676+=+676+-+576+\"
\n" ); document.write( "\"+z%5E2+-+52z+%2B+676+=+100+\"
\n" ); document.write( "\"+%28+z+-+26+%29%5E2+=+10%5E2+\"
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( "\"+z+-+26+=+10+\"
\n" ); document.write( "\"+z+=+36+\"
\n" ); document.write( "------------
\n" ); document.write( "also, using the negative square root of \"+100+\",.
\n" ); document.write( "\"+z+-+26+=+-10+\"
\n" ); document.write( "\"+z+=+16+\"
\n" ); document.write( "---------------
\n" ); document.write( "Now go back to
\n" ); document.write( "\"+x%5E2+=+z+\"
\n" ); document.write( "\"+x%5E2+=+36+\"
\n" ); document.write( "\"+x+=+6+\"
\n" ); document.write( "\"+x+=+-6+\"
\n" ); document.write( "and
\n" ); document.write( "\"+x%5E2+=+16+\"
\n" ); document.write( "\"+x+=+4+\"
\n" ); document.write( "\"+x+=+-4+\"
\n" ); document.write( "-------------
\n" ); document.write( "I get 4 real solutions,
\n" ); document.write( "\"+x+=+4+\"
\n" ); document.write( "\"+x+=+-4+\"
\n" ); document.write( "\"+x+=+6+\"
\n" ); document.write( "\"+x+=+-6+\"
\n" ); document.write( "--------------
\n" ); document.write( "You can check these by plugging back into equation
\n" ); document.write( "Here's the plot:
\n" ); document.write( "\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-150%2C+700%2C+x%5E4+-+52x%5E2+%2B+576+%29+\" \n" ); document.write( "
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