document.write( "Question 182224: Find all factors of x^2+x-12 \n" ); document.write( "

Algebra.Com's Answer #136749 by josmiceli(19441) $\"\"$ $\"About$

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$\"x%5E2+%2B+x+-+12\"$
\n" ); document.write( "If I set the equation equal to $\"0\"$ , I can use
\n" ); document.write( "the method of completing the square which says:
\n" ); document.write( "Take 1/2 of the coefficient of $\"x\"$ , square it,
\n" ); document.write( "and add it to both sides
\n" ); document.write( "First, add $\"12\"$ to both sides
\n" ); document.write( " $\"x%5E2+%2B+x+-+12+=+0\"$
\n" ); document.write( " $\"x%5E2+%2B+x+=+12\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2+%2B+x+%2B+%281%2F2%29%5E2+=+12+%2B+%281%2F2%29%5E2\"$
\n" ); document.write( " $\"x%5E2+%2B+x+%2B+1%2F4+=+12+%2B+1%2F4\"$
\n" ); document.write( " $\"%28x+%2B+1%2F2%29%5E2+=+49%2F4\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"x+%2B+1%2F2+=+7%2F2\"$
\n" ); document.write( " $\"x+=+6%2F2\"$
\n" ); document.write( "(a) $\"x+=+3\"$
\n" ); document.write( "Also I take the negative square root
\n" ); document.write( " $\"x+%2B+1%2F2+=+-%287%2F2%29\"$
\n" ); document.write( " $\"x+=+-%288%2F2%29\"$
\n" ); document.write( "(b) $\"x+=+-4\"$
\n" ); document.write( "Subtract $\"3\"$ from both sides of (a)
\n" ); document.write( " $\"x+-+3+=+0\"$
\n" ); document.write( "Add $\"4\"$ to both sides of (b)
\n" ); document.write( " $\"x+%2B+4+=+0\"$
\n" ); document.write( "Since these are both $\"0\"$ , their products is $\"0\"$
\n" ); document.write( " $\"%28x+-+3%29%28x+%2B+4%29+=+0\"$
\n" ); document.write( " $\"x%5E2+%2B+x+-+12+=+0\"$
\n" ); document.write( "The factors are $\"x-3\"$ and $\"x%2B4\"$ \n" ); document.write( "

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