SOLUTION: Hello, please help!! The sum of the squares of two numbers is 106. The sum of the two numbers is -4. Find the two numbers? Thank you!!!

Algebra ->  Equations -> SOLUTION: Hello, please help!! The sum of the squares of two numbers is 106. The sum of the two numbers is -4. Find the two numbers? Thank you!!!      Log On


   

Question 1008272: Hello, please help!!
The sum of the squares of two numbers is 106. The sum of the two numbers is -4. Find the two numbers?
Thank you!!!
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x%5E2%2By%5E2=106%2Cx%2By=-4%29

y=-x-4
-
substitute this into the squares equation.
x%5E2%2B%28-x-4%29%5E2=106
x%5E2%2B%28-1%29%5E2%28x%2B4%29%5E2=106
x%5E2%2B1%2A%28x%2B4%29%5E2=106
x%5E2%2Bx%5E2%2B8x%2B16=106
2x%5E2%2B8x%2B16=106
x%5E2%2B4x%2B8=53
x%5E2%2B4x%2B8-53=0
x%5E2%2B4x-45=0
%28x-5%29%28x%2B9%29=0

x can be either 5 or -9.
Correspondingly,
y can be either -9 or 5.

The two numbers are 5 and -9
Because this will match the second part of the description: that the sum be NEGATIVE 4.