document.write( "Question 118520: use the quadratic formula to solve\r
\n" ); document.write( "\n" ); document.write( "-16y^2 -8y + 3 =0 \n" ); document.write( "
Algebra.Com's Answer #86657 by solver91311(24713)\"\" \"About 
You can put this solution on YOUR website!
\"-16y%5E2+-8y+%2B+3+=0\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"-16x%5E2%2B-8x%2B3+=+0\") has the following solutons:
\n" ); document.write( "
\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-8%29%5E2-4%2A-16%2A3=256\".
\n" ); document.write( "
\n" ); document.write( " Discriminant d=256 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--8%2B-sqrt%28+256+%29%29%2F2%5Ca\".
\n" ); document.write( "
\n" ); document.write( " \"x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+256+%29%29%2F2%5C-16+=+-0.75\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-8%29-sqrt%28+256+%29%29%2F2%5C-16+=+0.25\"
\n" ); document.write( "
\n" ); document.write( " Quadratic expression \"-16x%5E2%2B-8x%2B3\" can be factored:
\n" ); document.write( " \"-16x%5E2%2B-8x%2B3+=+-16%28x--0.75%29%2A%28x-0.25%29\"
\n" ); document.write( " Again, the answer is: -0.75, 0.25.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B-8%2Ax%2B3+%29\"
\n" ); document.write( " \n" ); document.write( "
\n" );