document.write( "Question 578740: X{X-5}=8+(X-3)
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #370757 by edjones(8007)\"\" \"About 
You can put this solution on YOUR website!
X{X-5}=8+(X-3)
\n" ); document.write( "x^2-5x=8+x-3
\n" ); document.write( "x^2-6x-5=0
\n" ); document.write( "x=3-sqrt(14), x=3+sqrt(14) (see below)
\n" ); document.write( ".
\n" ); document.write( "Ed
\n" ); document.write( ".
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B-6x%2B-5+=+0\") has the following solutons:
\n" ); document.write( "
\n" ); document.write( " \"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
\n" ); document.write( "
\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-6%29%5E2-4%2A1%2A-5=56\".
\n" ); document.write( "
\n" ); document.write( " Discriminant d=56 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28--6%2B-sqrt%28+56+%29%29%2F2%5Ca\".
\n" ); document.write( "
\n" ); document.write( " \"x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+56+%29%29%2F2%5C1+=+6.74165738677394\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%28-6%29-sqrt%28+56+%29%29%2F2%5C1+=+-0.741657386773941\"
\n" ); document.write( "
\n" ); document.write( " Quadratic expression \"1x%5E2%2B-6x%2B-5\" can be factored:
\n" ); document.write( " \"1x%5E2%2B-6x%2B-5+=+1%28x-6.74165738677394%29%2A%28x--0.741657386773941%29\"
\n" ); document.write( " Again, the answer is: 6.74165738677394, -0.741657386773941.\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-6%2Ax%2B-5+%29\"
\n" ); document.write( " \n" ); document.write( "
\n" );