Solve x^2+ax+ageq0

$$x ^ { 2 } + a x + a \geq 0$$

Solve for x

$$\left\{\begin{matrix}x\in \mathrm{R}\text{, }&a\geq 0\text{ and }a\leq 4\\x\in (-\infty,\frac{-\sqrt{a(a-4)}-a}{2}]\cup [\frac{\sqrt{a(a-4)}-a}{2},\infty)\text{, }&a\geq 4\text{ or }a\leq 0\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a\leq -\frac{x^{2}}{x+1}\text{, }&x<-1\\a\geq -\frac{x^{2}}{x+1}\text{, }&x>-1\\a\in \mathrm{R}\text{, }&x=-1\\a=-\frac{x^{2}}{x+1}\text{, }&x\neq -1\end{matrix}\right.$$