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To find two numbers that multiply to 100 and add up to -20, we need to solve a system of equations. Let's denote the two numbers as x and y. We have the equations xy = 100 and x + y = -20. By substituting y = -20 - x into the first equation, we get x(-20 - x) = 100. Solving this quadratic equation gives us the two numbers as -10 and -10.