Posted by Chris on Tuesday, March 9, 2010 at 8:07am.
First of all, recognize that the point cannot be between x = 0 and x = 5, because the E fields due to the two particles will be in the same direction and cannot cancel each other. In the x > 5 region, the E field due to the -2 uC charge will be less everywhere, so camncellation is not possible. The location will have to be in the x <0 region.
In the x < 0 region,
-2 k/ x^2 + 5k /(5-x)^2 = 0
5/(5-x)^2 = 2/x^2
5x^2 = 50 -20x +2x^2
3x^2 +20x -45 = 0
Take the root x that is < 0. This does not factor easily.
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