Distance between point charges in equilibrium (simple)

[Mitocarta]

Homework Statement

Two fixed charges, +1.07 uC and -3.28 uC, are 61.8 cm apart. Where may a third charge be located so that no net force acts on it?

Homework Equations

Coulombs law

The Attempt at a Solution

q1 = 1.07 uC
q2 = -3.28 uC
q3 = q

q1 ----- q2 ----- q

q1 and q2 are separated by 0.618 m and q2 and q are separated by x

Since the charges are in equilibrium,


0 = k (1.07E-6)(q) / (0.618+x)^2 + k(1.07E-6)(q) / (x)^2

factoring out and eliminating k and q,

(1.07E-6)/(0.618+x)^2 + (3.28E-6)/(x)^2 = 0

Solving for x gives me an imaginary distance. I feel like this is a very simple problem but I can't spot my error. What am I doing incorrectly? Thank you for your time.

 

[TSny]

Hello Mitocarta, welcome to PF!

You've placed q closer to the larger magnitude charge. Is that going to work?

 

[Mitocarta]

Hello Mitocarta, welcome to PF!

You've placed q closer to the larger magnitude charge. Is that going to work?

Thank you for replying. When I switch the charges,

(3.28E-6)/(0.618+x)^2 + (1.07E-6)/(x)^2 = 0

I still get an imaginary answer.
Edit: Is there a way to input math in an easier to read format on this forum?

 

[TSny]

The two forces act in opposite directions on q. The net force will be zero if the magnitudes of the forces are equal to each other.

 

[Mitocarta]

The two forces act in opposite directions on q. The net force will be zero if the magnitudes of the forces are equal to each other.

Oh I was overlooking that! Thank you so much, got the correct answer.