document.write( "Question 501819: x^-6 - 11x^-3 + 24 = 0\r
\n" ); document.write( "\n" ); document.write( "I'm confused as to where to start!\r
\n" ); document.write( "\n" ); document.write( "Thanks,
\n" ); document.write( "Tracy \n" ); document.write( "
Algebra.Com's Answer #338689 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
x^-6 - 11x^-3 + 24 = 0
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\n" ); document.write( "Let y = x^-3
\n" ); document.write( "then
\n" ); document.write( "y^2 = x^-6
\n" ); document.write( ".
\n" ); document.write( "So, instead of:
\n" ); document.write( "x^-6 - 11x^-3 + 24 = 0
\n" ); document.write( "we can write:
\n" ); document.write( "y^2 - 11y + 24 = 0
\n" ); document.write( "now, we can factor the left:
\n" ); document.write( "(y-3)(y-8) = 0
\n" ); document.write( "y = {3, 8}
\n" ); document.write( "But, we're looking for 'x' NOT 'y', so substitute back into:
\n" ); document.write( "y = x^-3
\n" ); document.write( "3 = x^-3
\n" ); document.write( "3 = 1/x^3
\n" ); document.write( "3x^3 = 1
\n" ); document.write( "x^3 = 1/3
\n" ); document.write( "x = cuberoot(1/3)
\n" ); document.write( "or, rationalizing
\n" ); document.write( "x = cuberoot(3)/3
\n" ); document.write( "and, similarly
\n" ); document.write( "x = cuberoot(8)/8 = 2/8 = 1/4\r
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