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Let label one of the numbers with x, and the other one with y. So,
xy = -240
x + y = 8
y = 8 - x substitute this into the first equation;
x(8 - x) = -240
8x - x^2 = - 240
-x^2 + 8x + 240 = 0 or multiplying by -1 both sides;
x^2 - 8x - 240 = 0
(x + 12)(x - 20) = 0
x + 12 = 0 or x - 20 = 0
x = -12 or x = 20
So these numbers are -12 and 20.
Check:
-12 + 20 = 8
(-12)(20) = -240
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