$\left\{\begin{matrix}a=\frac{\sqrt{2}x}{4}\text{, }&arg(x)<\pi \text{ or }x=0\\a=-\frac{\sqrt{2}x}{4}\text{, }&arg(x)\geq \pi \text{ or }x=0\end{matrix}\right.$

$x=-2\sqrt{2}a$
$x=2\sqrt{2}a\text{, }arg(a)<\pi \text{ or }a=0$

$\left\{\begin{matrix}a=-\frac{\sqrt{2}x}{4}\text{, }&x\leq 0\\a=\frac{\sqrt{2}x}{4}\text{, }&x\geq 0\end{matrix}\right.$

$x=2\sqrt{2}a$
$x=-2\sqrt{2}a\text{, }a\geq 0$