document.write( "Question 1086031: Sviatoslav solved the quadratic equation x^2-x-1=0 by completing the square. In the process, he came up with the equivalent equation (x+a)^2 = b, where a and b are constants.\r
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Algebra.Com's Answer #700131 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"x%5E2-x-1=0\"$ .....to complete square, recall $\"%28a-b%29%5E2=a%5E2-2ab%2Bb%5E2\"$ ;so, we need to add and subtract $\"b%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-x%2Bb%5E2%29-b%5E2-1=0\"$ .. ..since coefficients $\"a=1\"$ and $\"2ab=-1\"$ , we have $\"2%2A1%2Ab=-1\"$ -> $\"2b=-1\"$ -> $\"b=-1%2F2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-x%2B%28-1%2F2%29%5E2%29-%28-1%2F2%29%5E2-1=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-1%2F2%29%5E2-%281%2F4%29-1=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-1%2F2%29%5E2-1%2F4-4%2F4=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-1%2F2%29%5E2-5%2F4=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x-1%2F2%29%5E2=5%2F4\"$ \r
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