SOLUTION: I need to know how to set up this problem. The sum of two numbers is -17. Their product is 66. Find the numbers.

Question 440838: I need to know how to set up this problem.
The sum of two numbers is -17. Their product is 66. Find the numbers.
Found 2 solutions by unlockmath, htmentor:
Answer by unlockmath(1688) (Show Source): You can put this solution on YOUR website!
Hello,
Let's have the 2 numbers be represented by x & y. Now we can set up two equations as:
x+y=-17
xy=66
There you go. Now you and use substitution to figure out the values.
Make sense?
RJ
www.math-unlock.com
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let x, y be the two numbers.
Given:
x + y = -17
x*y = 66
From the 2nd equation, y = 66/x
Substitute this value for y in the 1st equation:
x + 66/x = -17
Multiply through by x:
x^2 + 66 = -17x -> x^2 + 17x + 66 = 0
Solve for x using the quadratic formula:
x = (-17 +- sqrt(17^2 - 264))/2 -> x = (-17 +- 5)/2
This gives x = -11, -6
Which means y = -6, -11
So the two numbers are: -6, -11
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