document.write( "Question 1193600: solve quadratic equation by factoring
\n" ); document.write( "x^2+15x=-50 \n" ); document.write( "

Algebra.Com's Answer #825643 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( " $\"x%5E2%2B15x=-50\"$

\n" ); document.write( "(1) Get all terms on one side of the equation (add 50 to both sides):

\n" ); document.write( " $\"x%5E2%2B15x%2B50=0\"$

\n" ); document.write( "(2) You want to factor this as the product of two linear expressions. The constant term is positive, so the signs of the two expressions are the same; and the linear term is positive, so the signs of the two expressions are both positive. So the factoring will be of the form

\n" ); document.write( " $\"%28x%2Ba%29%28x%2Bb%29=x%5E2%2B%28a%2Bb%29x%2Bab=x%5E2%2B15x%2B50\"$

\n" ); document.write( "So you want a and b to be two positive integers whose sum is 15 and whose product is 50 -- 5 and 10. So

\n" ); document.write( " $\"x%5E2%2B15x%2B50=%28x%2B5%29%28x%2B10%29=0\"$
\n" ); document.write( "The product is 0 if and only if one of the factors is 0:

\n" ); document.write( " $\"x%2B5=0\"$ --> $\"x=-5\"$ or $\"x%2B10=0\"$ --> $\"x=-10\"$

\n" ); document.write( "ANSWERS: x=-5 and x=-10

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