document.write( "Question 162890This question is from textbook Elementary and Intermediate
\n" ); document.write( ": Write a complete solution to each problem.
\n" ); document.write( "29.) The sum of two numbers is 4, and their product is -32. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #120055 by Earlsdon(6294) $\"\"$ $\"About$

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Let the two numbers be x and y.
\n" ); document.write( "From the problem statement, you can write:
\n" ); document.write( " $\"x%2By+=+4\"$ and $\"x%2Ay+=+-32\"$
\n" ); document.write( "Rewrite the first equation as:
\n" ); document.write( " $\"x+=+4-y\"$ and substitute this into the second equation to get:
\n" ); document.write( " $\"%284-y%29%2A%28y%29+=+-32\"$ Simplify.
\n" ); document.write( " $\"4y-y%5E2+=+-32\"$ Rewrite as:
\n" ); document.write( " $\"y%5E2-4y-32+=+0\"$ Solve this quadratic equation by factoring.
\n" ); document.write( " $\"%28y%2B4%29%28y-8%29+=+0\"$ Apply the zero product rule.
\n" ); document.write( " $\"y%2B4+=+0\"$ or $\"y-8+=+0\"$ therefore...
\n" ); document.write( " $\"y+=+-4\"$ or $\"y+=+8\"$
\n" ); document.write( "To find x, substitute these values of y into: $\"x+=+4-y\"$
\n" ); document.write( " $\"x+=+4-%28-4%29\"$
\n" ); document.write( " $\"x+=+8\"$ and...
\n" ); document.write( " $\"x+=+4-8\"$
\n" ); document.write( " $\"x+=+-4\"$
\n" ); document.write( "The two numbers are -4 and 8
\n" ); document.write( "Check:
\n" ); document.write( " $\"-4%2B8+=+4\"$ Their sum is 4.
\n" ); document.write( " $\"%28-4%29%288%29+=+-32\"$ Their product is -32.
\n" ); document.write( " \n" ); document.write( "

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