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To find two numbers that multiply to 24 and add up to -14, we can set up a system of equations. Let's call the two numbers x and y. We have the equations xy = 24 and x + y = -14. By substituting y = -14 - x into the first equation, we get x(-14 - x) = 24. Simplifying this quadratic equation gives us x^2 + 14x + 24 = 0. Solving this quadratic equation will give us the two numbers that meet the given conditions.