Answer
$a = 4$
Work Step by Step
Because the net force is in the direction $45^{\circ}$ above the +x axis, the force on the $-q$ charge due to the $Q$ charge must be equal in magnitude to the force on the $-q$ charge due to the $+q$ charge.
We can find the value of $a$:
$\frac{k~(q)~(aq)}{(2L)^2} = \frac{kq^2}{L^2}$
$aq^2 = \frac{4L^2~q^2}{L^2}$
$a = 4$
