The equation of directrix of the parabola $y^{2} + 4y + 4x + 2 = 0$ is

We have, $y^{2} + 4y + 4x + 2 = 0$

$\Rightarrow (y + 2)^{2} + 4x - 2 = 0$

$\Rightarrow (y + 2)^{2} = -4\left (x - \dfrac {1}{2}\right )$

Replace, $y + 2 = Y, x - \dfrac {1}{2} = X$

We have, $Y^{2} = -4X$

This is a parabola with directrix at $X = 1$

$\Rightarrow x - \dfrac {1}{2} = 1$

$\Rightarrow x = \dfrac {3}{2}$.