document.write( "Question 474706: Find the roots of each equation using the Quadratic Formula\r
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Algebra.Com's Answer #325551 by jorel1380(3719)\"\" \"About 
You can put this solution on YOUR website!
1.) \"x%5E2%2B2x-24=0\"
\n" ); document.write( "\"%28x%2B6%29%28x-4%29=0\"
\n" ); document.write( "\"x=4+or+-6\"
\n" ); document.write( "2.) \"4x%2B32=x%5E2\"
\n" ); document.write( "\"x2-4x-32=0\"
\n" ); document.write( "\"%28x-8%29%28x%2B4%29=0\"
\n" ); document.write( "\"x=-4+or+8\"
\n" ); document.write( "3.) \"x%5E2-11x%2B30=0\"
\n" ); document.write( "\"%28x-5%29%28x-6%29=0\"
\n" ); document.write( "\"x=5+or+6\"..
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B2x%2B-24+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%282%29%5E2-4%2A1%2A-24=100\".
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\n" ); document.write( " Discriminant d=100 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-2%2B-sqrt%28+100+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%282%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+4\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%282%29-sqrt%28+100+%29%29%2F2%5C1+=+-6\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B2x%2B-24\" can be factored:
\n" ); document.write( " \"1x%5E2%2B2x%2B-24+=+1%28x-4%29%2A%28x--6%29\"
\n" ); document.write( " Again, the answer is: 4, -6.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-24+%29\"

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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-4x%2B-32+=+0\") has the following solutons:
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\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-4%29%5E2-4%2A1%2A-32=144\".
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\n" ); document.write( " Discriminant d=144 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--4%2B-sqrt%28+144+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+144+%29%29%2F2%5C1+=+8\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-4%29-sqrt%28+144+%29%29%2F2%5C1+=+-4\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-4x%2B-32\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-4x%2B-32+=+1%28x-8%29%2A%28x--4%29\"
\n" ); document.write( " Again, the answer is: 8, -4.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-32+%29\"

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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-11x%2B30+=+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=%28-11%29%5E2-4%2A1%2A30=1\".
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\n" ); document.write( " Discriminant d=1 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--11%2B-sqrt%28+1+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+6\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-11%29-sqrt%28+1+%29%29%2F2%5C1+=+5\"
\n" ); document.write( "
\n" ); document.write( " Quadratic expression \"1x%5E2%2B-11x%2B30\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-11x%2B30+=+1%28x-6%29%2A%28x-5%29\"
\n" ); document.write( " Again, the answer is: 6, 5.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-11%2Ax%2B30+%29\"
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