Solve for x
\left\{\begin{matrix}x=-1\text{, }&a>0\text{ and }a\leq 1\\x\in [-\frac{\sqrt{2}(\sqrt{(1-a)(a+2)}+\sqrt{2})}{2a},\frac{\sqrt{2(1-a)(a+2)}-2}{2a}]\text{, }&(a>0\text{ and }a<1)\text{ or }a=-2\\x\leq -\frac{1}{4}\text{, }&a\geq -2\text{ and }a\leq 0\\x\in [-\frac{\sqrt{2}(\sqrt{(1-a)(a+2)}+\sqrt{2})}{2a},\infty)\cup (-\infty,\frac{\sqrt{2(1-a)(a+2)}-2}{2a}]\text{, }&a\geq -2\text{ and }a<0\\x\in \mathrm{R}\text{, }&a\leq -2\end{matrix}\right.
Solve for a
a\leq -\frac{4x+1}{2x^{2}+1}
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