I'm stuck on a physics problem involving the net force of gravity on an object x kilometers away from Earth. The correct answer is 42000 km though I cannot seem to get it when I do the calculations. If someone could tell me where I am going wrong I would appreciate it. Note: I've tried several other problems just like this (albeit with different masses) so I don't think it's just a minor error that is causing my calculations to be way off - rather an error in thelogic.

Here is the problem, along with my work:

Take mass of Earth ME = 6.00 x 10^24 kg; mass of Mars MM = 6.42 x 10^23 kg; and the distance between their centres REM = 5.57 x 10^7 m. At what point (in km from Earth) between Earth and Mars is the net force of gravity on a body by both Earth and Mars exactly zero?

Let x = the distance of the object from earth

Let m = the mass of the object

$${F_E} = \frac{G\cdot {M_E}\cdot m}{x^2} = \frac{(6.674 x 10^{-11})(6.00 x 10^{24})(m)}{x^2}$$

$${F_M} = \frac{G\cdot {M_M}\cdot m}{(5.57 x 10^7- x)^2} = \frac{(6.674 x 10^{-11})(6.42 x 10^{23})(m)}{(5.57 x 10^7 - x)^2}$$

Set ${F_E} = {F_M}$ ... I have no idea why the TeX below doesn't work as it's literally the same code copied from the above.

$$\frac{(6.674 x 10^{-11})(6.00 x 10^{24})(m)}{x^2} = \frac{(6.674 x 10^{-11})(6.42 x 10^{23})(m)}{(5.57 x 10^7 - x)^2}$$

Divide out the gravitational constant (6.674 x 10^-11), the object massm, and the 10^24 and 10^23.

$$\frac{6}{x^2} = \frac{6.42}{(5.57 x 10^7 - x)^2}$$

$$(\frac{(5.57 x 10^7 - x)}{x})^2 = \frac{6.42}{6}$$

Take square root of both sides and I'm left with:

$$\frac{55700000 - x}{x} = 1.0344$$

Multiply both sides by x to get rid of it in the denominator on the left:

$$55700000 - x = 1.0344x$$

Add x to both sides, then divide to get x on its own:

$$x = 27379079.82$$

The answer I get (2.73 x 10^6) is way off and I don't know why. I've tried multiple times to isolate x in different ways but I always end up with a massive number instead of the 42000 km that is the answer. Any idea why?