Answer
$x = -0.691~m$
Work Step by Step
We can find the negative x coordinate where the net electric field is zero:
$E_{net} = \frac{\sigma}{2\epsilon_0}+\frac{Q}{4\pi~\epsilon_0~x^2} = 0$
$-\frac{\sigma}{2\epsilon_0} = \frac{Q}{4\pi~\epsilon_0~x^2}$
$-\sigma = \frac{Q}{2\pi~x^2}$
$x^2 = -\frac{Q}{2\pi~\sigma}$
$x = -\sqrt{-\frac{Q}{2\pi~\sigma}}$
$x = -\sqrt{-\frac{6.00~\mu C}{(2\pi)~(-2.00~\mu C/m^2)}}$
$x = -\sqrt{0.477465~m^2}$
$x = -0.691~m$
