document.write( "Question 465492: im looking for the explanations of this problem
\n" ); document.write( " 3x^2+12x+31=0 \n" ); document.write( "

Algebra.Com's Answer #318998 by Alan3354(69443) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"3x%5E2%2B12x%2B31+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%2812%29%5E2-4%2A3%2A31=-228\"$ .
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\n" ); document.write( " The discriminant -228 is less than zero. That means that there are no solutions among real numbers.

\n" ); document.write( " If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

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\n" ); document.write( " In the field of imaginary numbers, the square root of -228 is + or - $\"sqrt%28+228%29+=+15.0996688705415\"$ .
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\n" ); document.write( " The solution is

, or
\n" ); document.write( " Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B12%2Ax%2B31+%29\"$

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