document.write( "Question 989581: solve this equation x^2-2x+5=0 in the complex number system. \n" ); document.write( "
Algebra.Com's Answer #609865 by Alan3354(69443)\"\" \"About 
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solve this equation x^2-2x+5=0 in the complex number system.
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-2x%2B5+=+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%2A1%2A5=-16\".
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\n" ); document.write( " The discriminant -16 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 -16 is + or - \"sqrt%28+16%29+=+4\".
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\n" ); document.write( " The solution is \"x%5B12%5D+=+%28--2%2B-i%2Asqrt%28+-16+%29%29%2F2%5C1+=++%28--2%2B-i%2A4%29%2F2%5C1+\", or
\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-2%2Ax%2B5+%29\"

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\n" ); document.write( "\"+x+=+1+%2B-+2i\"
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