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There are one positive charge +3Q and one negative charge −Q which are fixed on the...

There are one positive charge +3Q and one negative charge −Q which are fixed on the x-axis with coordinate (−d,0) and (d,0) respectively. We would like to place a third one, carrying +2Q, at some place such that the net electric force on it is zero.

I said that the third charge should be placed to the right of the negative charge (-Q) so that the +3Q and -Q charges are canceling out.

k(3Q)(Q)/(x^2) = k(2Q)(Q)/(x-2d)^2

distance from 3Q to the third charge is x, and so the distance from -Q to 2Q should be (x-2d). The answer I get is (3+sqrt(3)) but the answer on the key says (2+sqrt(2)).

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