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

x + y = 4

xy = - 12

Using x + y = 4 to express y via x we have: y = 4 - x

Plug y = 4 - x into xy = -12:

x(4 - x) = -12

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click here to see the equation solved for x

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x1 = 6

x2 = -2

For x = 6 we have y = 4 - 6 that is y = -2.

For x = -2 we have y = 4 - (-2) that is y = 6.

The two numbers are 6 and -2.