Thomas M. answered • 08/09/16

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For f(-2): (-8 -(-2) -8) = -14

Since f(3) = 16, and f(2) = -2 and f(-2) = -14, there will be some value x such that f(x) = 0. And, since the function is a polynomial, it will be continuous in the interval [-2,3]. Therefore, the function x^3=x+8 does, in fact, have a real solution.