What Two Numbers Multiplied Equal 72 But When Added Equal -42?


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Let x be one of the numbers. Y will be the other for now.
Then since we know xy = 72, we can solve for y, and now think of it as (72/x).
Our other piece of information yields the equation: X + y = -42.
We can only solve for one variable at a time, so we need to write this second equation in terms of just one variable, x:
X + (72/x) = -42.
I like to clear the fractions first, so let's multiply everything on both sides by the LCD, x:
X^2 + 72 = -42x
X^2 +42x -72 = 0
We would have to use the quadratic formula to solve for x.
This yields two non-integer values for x, and since I'm assuming we need integers, there is no simple solution.

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