Chapter 1.5, Problem 136E

Gravity If an imaginary line segment is drawn between the centers of the earth and the moon, then the net gravitational force F acting on an object situated on this line segment is

$F=\frac{-K}{x^2}+\frac{0.012K}{{(239-x)}^2}$

where K > 0 is a constant and x is the distance of the object from the center of the earth, measured in thousands of miles. How far from the center of the earth is the “dead spot” where no net gravitational force acts upon the object? (Express your answer to the nearest thousand miles.)