document.write( "Question 630080: using the Quadratic Formula \n" ); document.write( "how can i solve \n" ); document.write( "½x^2 + x = 1 \n" ); document.write( "
Algebra.Com's Answer #396702 by richwmiller(17219)\"\" \"About 
You can put this solution on YOUR website!
multiply by 2 to make it easier to work with.
\n" ); document.write( "x^2+2x=2
\n" ); document.write( "x^2+2x-2=0
\n" ); document.write( "now use the quadratic formula
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ax%5E2%2Bbx%2Bc=0\" (in our case \"1x%5E2%2B2x%2B-2+=+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=%282%29%5E2-4%2A1%2A-2=12\".
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\n" ); document.write( " Discriminant d=12 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-2%2B-sqrt%28+12+%29%29%2F2%5Ca\".
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\n" ); document.write( " \"x%5B1%5D+=+%28-%282%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+0.732050807568877\"
\n" ); document.write( " \"x%5B2%5D+=+%28-%282%29-sqrt%28+12+%29%29%2F2%5C1+=+-2.73205080756888\"
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\n" ); document.write( " Quadratic expression \"1x%5E2%2B2x%2B-2\" can be factored:
\n" ); document.write( " \"1x%5E2%2B2x%2B-2+=+1%28x-0.732050807568877%29%2A%28x--2.73205080756888%29\"
\n" ); document.write( " Again, the answer is: 0.732050807568877, -2.73205080756888.\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%2B2%2Ax%2B-2+%29\"
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