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Finding electric charge on each sphere: given total charge

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Each of two small spheres is charged positively, the combined charge being 5 x 10^-5 C. If each sphere is repelled from the other by a force of one newton, when the spheres are two meters apart, how is the total charge distributed between the two spheres ?

https://brainmass.com/physics/electric/finding-electric-charge-sphere-given-total-charge-7410

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Let q1 and q2 be the charge on the two spheres.

q1 + q2 = 5 x 10^-5 C .........(1)

we have , F = K (q1 q2/R^2)

where K = 9 x 10^9 and R = 2

therefore,
1 newton = K (q1 q2/R^2)

= 9 x 10^9 (q1 q2/2^2)

from this q1q2 = (4/9) x 10^-9

We can write, (A-B)^2 = (A+B)^2 - 4 (A B)

therefore, (q1-q2)^2 = (q1+q2)^2 - 4 q1 q2

= 25 X 10^-10 - (16/9) X 10^-9

= [25 - (160/9)] X 10^-10

OR,
q1 - q2 = 2.69 x 10^-5 Coulomb .........(2)

from (1) & (2) we get,

q1 = 3.85 x 10^-5 C and

q2 = 1.15 x 10^-5 C

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