Let 'x' and 'y' represent the two numbers.

xy = 49

x + y = -50

y = - 50 - x

Plug y = - 50 - x into xy = 49:

x(- 50 - x) = 49

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click here to see the equation solved for x

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x1 = -1

x2 = -49

For x = -1 we have y = -50-(-1) = -49.

For x = -49 we have y = -50 - (-49) = -1. 

The two numbers are -1 and -49.