document.write( "Question 574550: what is exact value of the only real root of the equation x^3 + 6x^2 + 12x + 24 = 0 \n" ); document.write( "

Algebra.Com's Answer #369186 by KMST(5328) $\"\"$ $\"About$

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When you look at $\"x%5E3+%2B+6x%5E2+%2B+12x+%2B+24+=+0\"$ , it may remind you of
\n" ); document.write( " $\"%28x%2B2%29%5E3=x%5E3%2B6x%5E2%2B12x%2B8\"$ , so we could \"complete the cube\"
\n" ); document.write( " $\"x%5E3+%2B+6x%5E2+%2B+12x+%2B+24+=+0\"$ --> $\"x%5E3+%2B+6x%5E2+%2B+12x+=+-24\"$ --> $\"x%5E3+%2B+6x%5E2+%2B+12x+%2B8=+-24%2B8\"$ --> $\"%28x%2B2%29%5E3=-16\"$
\n" ); document.write( "The only real solution is $\"x%2B2=root%283%2C16%29\"$ , so
\n" ); document.write( " $\"highlight%28x=-2-root%283%2C16%29%29\"$ \n" ); document.write( "

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