document.write( "Question 542130: I need help finding the answer to \"2%2F%285x%29+%2B+1+=+1%2F3+%2B+x\" \n" ); document.write( "
Algebra.Com's Answer #356035 by JBarnum(2146)\"\" \"About 
You can put this solution on YOUR website!
\"2%2F%285x%29+%2B+1+=+1%2F3+%2B+x\"
\n" ); document.write( "\"2%2F%285x%29+%2B+3%2F3+=+1%2F3+%2B+x\"
\n" ); document.write( "\"2%2F%285x%29+%2B+2%2F3+=+x\"
\n" ); document.write( "\"%282%2F%285x%29%29%283%2A5x%29+%2B+2%2F3%283%2A5x%29+=+x%283%2A5x%29\" multiply by common denom
\n" ); document.write( "\"6%2B10x=15x%5E2\" put in quadratic equation form
\n" ); document.write( "\"0=15x%5E2-10x-6\" solve quadratic equation
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"15x%5E2%2B-10x%2B-6+=+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=%28-10%29%5E2-4%2A15%2A-6=460\".
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\n" ); document.write( " Discriminant d=460 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--10%2B-sqrt%28+460+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+460+%29%29%2F2%5C15+=+1.04825368631757\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-10%29-sqrt%28+460+%29%29%2F2%5C15+=+-0.381587019650907\"
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\n" ); document.write( " Quadratic expression \"15x%5E2%2B-10x%2B-6\" can be factored:
\n" ); document.write( " \"15x%5E2%2B-10x%2B-6+=+15%28x-1.04825368631757%29%2A%28x--0.381587019650907%29\"
\n" ); document.write( " Again, the answer is: 1.04825368631757, -0.381587019650907.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-10%2Ax%2B-6+%29\"

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