document.write( "Question 864704: solve\r
\n" ); document.write( "\n" ); document.write( "log (x+2) + log (2x-3) =2 x>0
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Algebra.Com's Answer #521204 by ewatrrr(24785)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "Hi
\n" ); document.write( "log (x+2) + log (2x-3) =2
\n" ); document.write( "log (x+2)(2x-3) = 2
\n" ); document.write( "(x+2)(2x-3) = 100
\n" ); document.write( " 2x^2 +x -100 = 0
\n" ); document.write( "x = 6.82548584904245 x > 0
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"2x%5E2%2B1x%2B-100+=+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=%281%29%5E2-4%2A2%2A-100=801\".
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\n" ); document.write( " Discriminant d=801 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-1%2B-sqrt%28+801+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%281%29%2Bsqrt%28+801+%29%29%2F2%5C2+=+6.82548584904245\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%281%29-sqrt%28+801+%29%29%2F2%5C2+=+-7.32548584904245\"
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\n" ); document.write( " Quadratic expression \"2x%5E2%2B1x%2B-100\" can be factored:
\n" ); document.write( " \"2x%5E2%2B1x%2B-100+=+2%28x-6.82548584904245%29%2A%28x--7.32548584904245%29\"
\n" ); document.write( " Again, the answer is: 6.82548584904245, -7.32548584904245.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B1%2Ax%2B-100+%29\"
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