Question on gravitational field

[gaobo9109]

Homework Statement

Considering only the gravitational fields of the Earth and the Moon, find the distance from the Earth at which a space capsule traveling between the Earth and the Moon is subject to zero gravitational force.

Mass of the Earth = 5.98 x 10²⁴kg
Mass of the Moon = 7.35 x 10²²kg
Radius of Moon's orbit = 3.84 x 10⁸m
Radius of the Earth = 6.38 x 10⁶m
Radius of the Moon = 1.74 x 10⁶m

Homework Equations

The Attempt at a Solution

Let x be the distance between the centre of Earth and the point of zero gravitational field

Gravitational field due to Earth = Gravational field due to Moon
GM_E/x² = GM_M/(R - x)²
(M_E/M_M)^1/2=x/(R-x)
x = (M_E/M_M)^1/2R/((M_E/M_M)^1/2 +1)
= 3.79 x 10⁸

But the answer provided is 3.46 x 10⁸

Can anyone tell me where I went wrong?

 

[Filip Larsen]

Since the symbolic result is correct you must have made an error during the actual calculation of the number.