Two small nonconducting spheres have a total charge of 86.9?C. When placed 1.11

Question

Two small nonconducting spheres have a total charge of 86.9?C. When placed 1.11 m apart, the force each exerts on the other is 11.1 N and is repulsive. What is the (larger) charge on the spheres? What is the smaller charge of the spheres?

Not sure what I am doing wrong. I re-wrote the equation F=kq/r^2 to solve for q.

q^2 = Fr^2/k ---------- (11.1)(1.11^2) / (8.99x10 ^3) = 0.00152. (converted K from 10^9 to 10^3 to compensate for the charge being in micro).

Then I used the quadratic formula to solve the problem: q^2 - 86.9q+ 0.00152. The answer I came up with is 86.9 and 1.7x10^-5 and it is wrong. Can someone please explain to me where I am making a mistake?

Explanation / Answer

let the one charge be x then second charge is 86.9-x

k*q*Q/(r^2) = F

9*10^(9)*x*(89.6-x)/(1.11^2) = 11.1

x*(89.6 - x) = 1.52*10^(-9)

as x is in micro columb

x*(89.6-x)*10^(-12) = 1.52*10^(-9)

89.6x-x^2 = 1519.69

x^2 - 89.6x +1519.59 = 0

x = 66.87
or 22.72

smaller charge be 22.72 then larger is 66.88

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