document.write( "Question 643589: solve for x: 4x=-5x^2 +2x^3 \n" ); document.write( "

Algebra.Com's Answer #404553 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"4x=-5x%5E2+%2B2x%5E3\"$
\n" ); document.write( "For any polynomial equation of degree greater than 1, you want one side of the equation to be a zero. So we'll start by subtracting 4x from each side:
\n" ); document.write( " $\"+0=-5x%5E2+%2B2x%5E3-4x\"$

\n" ); document.write( "Before we factor, let's put the terms in order from highest exponent to lowest:
\n" ); document.write( " $\"+0=+2x%5E3-5x%5E2+-4x\"$
\n" ); document.write( "Now we factor. First the greatest common factor , GCF, which is x:
\n" ); document.write( " $\"+0=+x%282x%5E2-5x+-4%29\"$
\n" ); document.write( "This is as far as the expression will factor. From this and the Zero Product property we know that one of these factors must be zero. So
\n" ); document.write( " $\"x+=+0\"$ or $\"2x%5E2-5x-4+=+0\"$
\n" ); document.write( "To find the solutions to the second equation, we will use the Quadratic Formula:
\n" ); document.write( " $\"x+=+%28-%28-5%29%2B-sqrt%28%28-5%29%5E2-4%282%29%28-4%29%29%29%2F2%282%29\"$
\n" ); document.write( "Simplifying...
\n" ); document.write( " $\"x+=+%28-%28-5%29%2B-sqrt%2825-4%282%29%28-4%29%29%29%2F2%282%29\"$
\n" ); document.write( " $\"x+=+%28-%28-5%29%2B-sqrt%2825%2B32%29%29%2F2%282%29\"$
\n" ); document.write( " $\"x+=+%28-%28-5%29%2B-sqrt%2867%29%29%2F2%282%29\"$
\n" ); document.write( " $\"x+=+%285%2B-sqrt%2867%29%29%2F4\"$
\n" ); document.write( "which is short for:
\n" ); document.write( " $\"x+=+%285%2Bsqrt%2867%29%29%2F4\"$ or $\"x+=+%285-sqrt%2867%29%29%2F4\"$

\n" ); document.write( "So the three solutions are:
\n" ); document.write( " $\"x+=+0\"$ or $\"x+=+%285%2Bsqrt%2867%29%29%2F4\"$ or $\"x+=+%285-sqrt%2867%29%29%2F4\"$ \n" ); document.write( "

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