document.write( "Question 438459: Where do the two graphs \"f%28x%29=x%5E2%2B2\" and \"g%28x%29=x-8\" intersect? \n" ); document.write( "
Algebra.Com's Answer #303203 by Alan3354(69443)\"\" \"About 
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Where f(x) and g(x) are equal.
\n" ); document.write( "\"f%28x%29=x%5E2%2B2+=+g%28x%29=x-8\"
\n" ); document.write( "\"x%5E2+%2B+2+=+x+-+8\"
\n" ); document.write( "\"x%5E2+-+x+%2B+10+=+0\"
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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-1x%2B10+=+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=%28-1%29%5E2-4%2A1%2A10=-39\".
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\n" ); document.write( " The discriminant -39 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 -39 is + or - \"sqrt%28+39%29+=+6.2449979983984\".
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\n" ); document.write( " The solution is , 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-1%2Ax%2B10+%29\"

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\n" ); document.write( "The solutions are not real numbers, so the graphs do not intersect.
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