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To find two numbers that multiply to -54 and add up to -15, we need to solve a system of equations. Let the two numbers be x and y. We have the equations xy = -54 and x + y = -15. By substituting y = -15 - x into the first equation, we get x(-15 - x) = -54. Simplifying this equation gives us x^2 + 15x - 54 = 0. Factoring this quadratic equation, we find that the two numbers are -9 and 6.