First, we need to find the complementary function, which is the solution to the homogeneous equation: $x'' + 2x' + 50x = 0$. The characteristic equation is $r^2 + 2r + 50 = 0$. Using the quadratic formula, we get:
$r = \frac{-2 \pm \sqrt{(-2)^2 - 4(1)(50)}}{2(1)}
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