SOLUTION: What numbers add to make 10 and times to make -16

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Question 1210340: What numbers add to make 10 and times to make -16
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


Here is one of many ways to solve the problem.

Since the two numbers add to 10, let them be (5+a) and (5-a).

The product of the two numbers is -16:

%285%2Ba%29%285-a%29=-16
25-a%5E2=-16
41=a%5E2
a=sqrt%2841%29 or a=-sqrt%2841%29

ANSWERS: 5%2Bsqrt%2841%29 and 5-sqrt%2841%29

Answer by josgarithmetic(39631) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x%2By=10%2Cand%2Cxy=-16%29

y=10-x.
Substitute...
x%2810-x%29=-16
10x-x%5E2=-16
-10x%2Bx%5E2=16
x%5E2-10x-16=0

General Solution for Quadratic Equation
x=%2810%2B-+sqrt%28100%2B4%2A16%29%29%2F2 (some steps taken, not shown)
x=%2810%2B-+sqrt%28164%29%29%2F2
x=%2810%2B-+sqrt%284%2A41%29%29%2F2
x=5%2B-+sqrt%2841%29

and you can finish what this means.