document.write( "Question 18987: $\"z%5E2-13z%2B36=0\"$ \n" ); document.write( "

Algebra.Com's Answer #9114 by Alwayscheerful(414) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"az%5E2%2Bbz%2Bc=0\"$ (in our case $\"1z%5E2%2B-13z%2B36+=+0\"$ ) has the following solutons:
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\n" ); document.write( " $\"z%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
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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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-13%29%5E2-4%2A1%2A36=25\"$ .
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\n" ); document.write( " Discriminant d=25 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--13%2B-sqrt%28+25+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"z%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+25+%29%29%2F2%5C1+=+9\"$
\n" ); document.write( " $\"z%5B2%5D+=+%28-%28-13%29-sqrt%28+25+%29%29%2F2%5C1+=+4\"$
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\n" ); document.write( " Quadratic expression $\"1z%5E2%2B-13z%2B36\"$ can be factored:
\n" ); document.write( " $\"1z%5E2%2B-13z%2B36+=+1%28z-9%29%2A%28z-4%29\"$
\n" ); document.write( " Again, the answer is: 9, 4.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-13%2Ax%2B36+%29\"$

\n" ); document.write( "\n" ); document.write( "Hope this helps! \n" ); document.write( "

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