document.write( "Question 113859: Solve the following: x^3 + 2x^2 = -5x \n" ); document.write( "
Algebra.Com's Answer #83621 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"x%5E3%2B2x%5E2=-5x\" Start with the given equation\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x%5E3%2B2x%5E2%2B5x=0\" Move all of the terms to the left side\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x%28x%5E2%2B2x%2B5%29=0\" Factor out the GCF \"x\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x=0\" or \"x%5E2%2B2x%2B5=0\" Set each factor equal to zero\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So this means we have one solution of x=0\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's focus on the second equation \"x%5E2%2B2x%2B5=0\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for x:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Starting with the general quadratic\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"ax%5E2%2Bbx%2Bc=0\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "the general solution using the quadratic equation is:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So lets solve \"x%5E2%2B2%2Ax%2B5=0\" ( notice \"a=1\", \"b=2\", and \"c=5\")\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29\" Plug in a=1, b=2, and c=5\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B-+sqrt%28+4-4%2A1%2A5+%29%29%2F%282%2A1%29\" Square 2 to get 4 \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B-+sqrt%28+4%2B-20+%29%29%2F%282%2A1%29\" Multiply \"-4%2A5%2A1\" to get \"-20\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B-+sqrt%28+-16+%29%29%2F%282%2A1%29\" Combine like terms in the radicand (everything under the square root)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B-+4%2Ai%29%2F%282%2A1%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-2+%2B-+4%2Ai%29%2F%282%29\" Multiply 2 and 1 to get 2\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "After simplifying, the quadratic has roots of\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"x=-1+%2B+2%2Ai\" or \"x=-1+-+2%2Ai\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Notice if we graph the quadratic \"y=x%5E2%2B2%2Ax%2B5\", we get\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"+graph%28+500%2C+500%2C+-16%2C+14%2C+-11%2C+19%2C+x%5E2%2B2%2Ax%2B5%29+\" graph of \"y=x%5E2%2B2%2Ax%2B5\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "And we can see that there are no real roots\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To visually verify the answer, check out this page to see a visual representation of imaginary roots\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------------------------------------------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answer:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So we have the solutions : \"x=0\", \"x=-1+%2B+2%2Ai\" or \"x=-1+-+2%2Ai\"
\n" ); document.write( "
\n" ); document.write( "
\n" );