F = k*(q1)*(q2)/r^2
We know that:
F = 71 N
k = coulomb's constant = 9*10^9
q1 = ?
q2 = ?
We know that q1 = q2, since in the question it states that the charges are identical.
r = 0.99 m
F = k*(q1)*(q1)/r^2
F = k*(q1)^2/r^2
71 = 9*10^9 * (q1)^2 / 0.99^2
Isolating (q1)^2,
71 * 0.99^2 / (9*10^9) = (q1)^2
Taking square root of both sides to get q1 to the power of 1,
sqrt( 71 * 0.99^2 / (9*10^9) ) = q1
Now, simplifying the left side in a calculator, we get that
q1 = 8.793 * 10^-5 C = q2