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The numbers are 5 and -4.

Let the two numbers be x and y. Our two equations can then be written as:

xy = -20 and x + y = 1

x (1-x) = -20

x - x2 = -20

x2 - x = 20

x2 - x - 20 = 0 factors to (x+4)(x-5) = 0

Q: What two numbers multiply to give you -20 but add to give you positive 1?

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