document.write( "Question 58913: Solve:
\n" ); document.write( "4x^2+1=2x \n" ); document.write( "

Algebra.Com's Answer #40446 by aaaaaaaa(138) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"4x%5E2%2B1=2x\"$
\n" ); document.write( " $\"4x%5E2-2x%2B1=0\"$
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"4x%5E2%2B-2x%2B1+=+0\"$ ) 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 $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%28-2%29%5E2-4%2A4%2A1=-12\"$ .
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\n" ); document.write( " The discriminant -12 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 -12 is + or - $\"sqrt%28+12%29+=+3.46410161513775\"$ .
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\n" ); document.write( " The solution is

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\n" ); document.write( " Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-2%2Ax%2B1+%29\"$

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