SOLUTION: Write a complete solution to each problem. 29.) The sum of two numbers is 4, and their product is -32. Find the numbers.

Algebra ->  Test -> SOLUTION: Write a complete solution to each problem. 29.) The sum of two numbers is 4, and their product is -32. Find the numbers.      Log On


   

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

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be x and y.
From the problem statement, you can write:
x%2By+=+4 and x%2Ay+=+-32
Rewrite the first equation as:
x+=+4-y and substitute this into the second equation to get:
%284-y%29%2A%28y%29+=+-32 Simplify.
4y-y%5E2+=+-32 Rewrite as:
y%5E2-4y-32+=+0 Solve this quadratic equation by factoring.
%28y%2B4%29%28y-8%29+=+0 Apply the zero product rule.
y%2B4+=+0 or y-8+=+0 therefore...
y+=+-4 or y+=+8
To find x, substitute these values of y into:x+=+4-y
x+=+4-%28-4%29
x+=+8 and...
x+=+4-8
x+=+-4
The two numbers are -4 and 8
Check:
-4%2B8+=+4 Their sum is 4.
%28-4%29%288%29+=+-32 Their product is -32.