document.write( "Question 30224: Use the quadratic formula
\n" ); document.write( "x^2+8x+7=0\r
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\n" ); document.write( "x^2+12m+11=0 \n" ); document.write( "

Algebra.Com's Answer #16923 by atif.muhammad(135) $\"\"$ $\"About$

You can put this solution on YOUR website!

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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"1x%5E2%2B8x%2B7+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%288%29%5E2-4%2A1%2A7=36\"$ .
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\n" ); document.write( " Discriminant d=36 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28-8%2B-sqrt%28+36+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%288%29%2Bsqrt%28+36+%29%29%2F2%5C1+=+-1\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%288%29-sqrt%28+36+%29%29%2F2%5C1+=+-7\"$
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\n" ); document.write( " Quadratic expression $\"1x%5E2%2B8x%2B7\"$ can be factored:
\n" ); document.write( " $\"1x%5E2%2B8x%2B7+=+1%28x--1%29%2A%28x--7%29\"$
\n" ); document.write( " Again, the answer is: -1, -7.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B7+%29\"$

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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"1x%5E2%2B12x%2B11+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%2812%29%5E2-4%2A1%2A11=100\"$ .
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\n" ); document.write( " Discriminant d=100 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28-12%2B-sqrt%28+100+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+-1\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%2812%29-sqrt%28+100+%29%29%2F2%5C1+=+-11\"$
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\n" ); document.write( " Quadratic expression $\"1x%5E2%2B12x%2B11\"$ can be factored:
\n" ); document.write( " $\"1x%5E2%2B12x%2B11+=+1%28x--1%29%2A%28x--11%29\"$
\n" ); document.write( " Again, the answer is: -1, -11.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B12%2Ax%2B11+%29\"$

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