document.write( "Question 685172: Evaluate and get exact answer for:
\n" ); document.write( "\"+10%5Ex+%2B+10%5E%28-x%29+=+48+\"
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Algebra.Com's Answer #424374 by Alan3354(69443)\"\" \"About 
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Evaluate and get exact answer for:
\n" ); document.write( "\"+10%5Ex+%2B+10%5E%28-x%29+=+48+\"
\n" ); document.write( "\"+10%5E%282x%29+%2B+1+=+48%2A10%5Ex+\"
\n" ); document.write( "\"+10%5E%282x%29+-+48%2A10%5Ex+%2B+1+=+0\"
\n" ); document.write( "u = 10^x
\n" ); document.write( "\"u%5E2+-+48u+%2B+1+=+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-48x%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=%28-48%29%5E2-4%2A1%2A1=2300\".
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\n" ); document.write( " Discriminant d=2300 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--48%2B-sqrt%28+2300+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-48%29%2Bsqrt%28+2300+%29%29%2F2%5C1+=+47.9791576165636\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-48%29-sqrt%28+2300+%29%29%2F2%5C1+=+0.0208423834364027\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B-48x%2B1\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-48x%2B1+=+%28x-47.9791576165636%29%2A%28x-0.0208423834364027%29\"
\n" ); document.write( " Again, the answer is: 47.9791576165636, 0.0208423834364027.\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-48%2Ax%2B1+%29\"

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\n" ); document.write( "10^x = 24 + sqrt(575)
\n" ); document.write( "x = log(24 + sqrt(575))
\n" ); document.write( "x = log(24 - sqrt(575))
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