document.write( "Question 881939: With f(x)=x^2-8x-1, find all values of x for which f(x)=0. \n" ); document.write( "

Algebra.Com's Answer #532616 by ewatrrr(24785) $\"\"$ $\"About$

You can put this solution on YOUR website!
f(x)=x^2-8x-1
\n" ); document.write( "x^2 - 8x - 1+ 0
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"1x%5E2%2B-8x%2B-1+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-8%29%5E2-4%2A1%2A-1=68\"$ .
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\n" ); document.write( " Discriminant d=68 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--8%2B-sqrt%28+68+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+68+%29%29%2F2%5C1+=+8.12310562561766\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%28-8%29-sqrt%28+68+%29%29%2F2%5C1+=+-0.123105625617661\"$
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\n" ); document.write( " Quadratic expression $\"1x%5E2%2B-8x%2B-1\"$ can be factored:
\n" ); document.write( " $\"1x%5E2%2B-8x%2B-1+=+1%28x-8.12310562561766%29%2A%28x--0.123105625617661%29\"$
\n" ); document.write( " Again, the answer is: 8.12310562561766, -0.123105625617661.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B-1+%29\"$

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