Write two numbers that multiply to the value on top and add to the value on bottom.
27
-12

-3 and -9

Step-by-step explanation:

First, it is helpful to write out what is given by the question, with variables x and y.

         x*y = 27

         x+y = -12

Now we will isolate a variable from one and plug it into the other:

         y = -12 - x

         x(-12-x) = 27

         -x^2 -12x -27 = 0

         x^2 + 12x + 27

         (x + 9) (x + 3) = 0

         x must be either -9 or -3

Now we plug those x-values into either equation to get their corresponding y-values:

         -9 + y = -12

         y = -3

         -3 + y = -12

         y = -9

We can see that the first x value (-9) corresponds to y = -3, and the second pair is -3 and -9. Either way, the pair is -3 and -9.

Therefore the pair of numbers must be -3 and -9.

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