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We can write the inequality as x2+6x−16>0. By the quadratic formula, the roots of this equation are [x = -6 \pm \sqrt{6^2 + 4(1)(-16)} = -6 \pm 2\sqrt{13}.]Since the coefficient of x2 is positive, the parabola opens upwards, so the roots divide the number line into three intervals:

-6 - 2√13 -6 + 2√13 -6

The inequality x(x+6)>16 is satisfied when x is in the middle interval, so the solution is [x \in \boxed{(-6 + 2\sqrt{13}, -6 - 2\sqrt{13})}.]

Guest Jul 17, 2023