document.write( "Question 22829: solve and write in simplest form\r
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Algebra.Com's Answer #11215 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 $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"1x%5E2%2B-4x%2B1+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-4%29%5E2-4%2A1%2A1=12\"$ .
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\n" ); document.write( " Discriminant d=12 is greater than zero. That means that there are two solutions: $\"+x%5B12%5D+=+%28--4%2B-sqrt%28+12+%29%29%2F2%5Ca\"$ .
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\n" ); document.write( " $\"x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+3.73205080756888\"$
\n" ); document.write( " $\"x%5B2%5D+=+%28-%28-4%29-sqrt%28+12+%29%29%2F2%5C1+=+0.267949192431123\"$
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\n" ); document.write( " Quadratic expression $\"1x%5E2%2B-4x%2B1\"$ can be factored:
\n" ); document.write( " $\"1x%5E2%2B-4x%2B1+=+1%28x-3.73205080756888%29%2A%28x-0.267949192431123%29\"$
\n" ); document.write( " Again, the answer is: 3.73205080756888, 0.267949192431123.\n" ); document.write( "Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B1+%29\"$

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

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