document.write( "Question 24213: r-6r^2 =-1 \n" ); document.write( "

Algebra.Com's Answer #12889 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 $\"ar%5E2%2Bbr%2Bc=0\"$ (in our case $\"-6r%5E2%2B1r%2B1+=+0\"$ ) has the following solutons:
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\n" ); document.write( " $\"r%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
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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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%281%29%5E2-4%2A-6%2A1=25\"$ .
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\n" ); document.write( " Discriminant d=25 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28-1%2B-sqrt%28+25+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"r%5B1%5D+=+%28-%281%29%2Bsqrt%28+25+%29%29%2F2%5C-6+=+-0.333333333333333\"$
\n" ); document.write( " $\"r%5B2%5D+=+%28-%281%29-sqrt%28+25+%29%29%2F2%5C-6+=+0.5\"$
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\n" ); document.write( " Quadratic expression $\"-6r%5E2%2B1r%2B1\"$ can be factored:
\n" ); document.write( " $\"-6r%5E2%2B1r%2B1+=+-6%28r--0.333333333333333%29%2A%28r-0.5%29\"$
\n" ); document.write( " Again, the answer is: -0.333333333333333, 0.5.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-6%2Ax%5E2%2B1%2Ax%2B1+%29\"$

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

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