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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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