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Write a quadratic equation with real coefficients if one of the solutions is -5 + 7i
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The quadratic equation with real coefficients that has a solution of -5 + 7i is x^2 + 10x + 41 = 0. This equation can be written using the factored form (x + 5 + 7i)(x + 5 - 7i) = 0. To solve a complex-number equation, you must set each factor equal to 0 and solve for x, which yields x = -5 ± 7i.
