Two nonconducting spheres problem

[n77ler]

Homework Statement

Two nonconducting spheres have a total charge of 13.4 μC. When placed 0.362 m apart. the force of repulsion is 2.777 N. What is the value of the greater charge (Give your answer in coulombs)?

Homework Equations

The Attempt at a Solution

 

[Doc Al]

Hint: Coulomb's law.

 

[n77ler]

I tried this equation below because I just put in the total charge for Q and got the wrong answer. I don't understand how I get answers for two different charge swhen I work through it.
E= k (q1+q2) / r^2

 

[tongpu]

well first equation is F = K(q1)(q2)/r^2 and second equation is q1q2=13.4 μC
2 equations 2 unknowns.

 

[Doc Al]

well first equation is F = K(q1)(q2)/r^2 and second equation is q1q2=13.4 μC
2 equations 2 unknowns.

You are correct, but that second equation has a typo: it should be q1 + q2 = 13.4 μC

 

[n77ler]

F=kq1q2 / r^2 q1 + q2 = 13.4x10^-6C
2.777= (8.99x10^9)q1q2 /(0.362)^2
q1q2=4.05x10^-11
q1=(4.05x10^-11)/ q2

(4.05x10^-11)/q2 + q2 = 13.4x10^-6C
(4.05x10^-11)/ q2 + (q2^2)/q2 = 13.4x10^-6C
(4.05x10^-11) + (q2^2) = (13.4x10^-6C)q2
quadratic, when solved q2=4.60x10^-6, q2= 8.80x10^-6

Both of these numbers when added up will equal the total charge and when I sub them into the equation q1=(4.05x10^-11)/q2 I get the same thing. However this is not the correct answer, could someone point out where I went wrong?