please explain the following:

correct answer is not indicated here due to some typo error. the solution for this problem is as follows:

let the charge at the origin be q. the force between the charge q and q1 is

f1 = k' q q1 / a²                                                                                

let k' = (1 / 4 x pi x episilon0)

the force between the charge q and q2 is

f2 = k' q q2 / (2a)²

since q1 = k q2

then    f1 = k' q k q2 / a²

f1 = 4 k f2

since the net force on origin is zero then

f1 + f2 = 0

4 k f2 + f2 = 0

k = - 1 / 4