Solve 2-x^2(1+a)^2+4a=0

$$2 - x ^ { 2 } ( 1 + a ) ^ { 2 } + 4 a = 0$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-1-\frac{\sqrt{4-2x^{2}}}{x^{2}}+\frac{2}{x^{2}}\text{; }a=-1+\frac{\sqrt{4-2x^{2}}}{x^{2}}+\frac{2}{x^{2}}\text{, }&x\neq 0\\a=-\frac{1}{2}=-0.5\text{, }&x=0\end{matrix}\right.$$

Solve for x (complex solution)

$$x=-\frac{i\sqrt{-4a-2}}{a+1}$$

$$x=\frac{i\sqrt{-4a-2}}{a+1}\text{, }a\neq -1$$

Solve for a

$$\left\{\begin{matrix}a=-1-\frac{\sqrt{4-2x^{2}}}{x^{2}}+\frac{2}{x^{2}}\text{; }a=-1+\frac{\sqrt{4-2x^{2}}}{x^{2}}+\frac{2}{x^{2}}\text{, }&x\neq 0\text{ and }|x|\leq \sqrt{2}\\a=-\frac{1}{2}=-0.5\text{, }&x=0\end{matrix}\right.$$

Solve for x

$$x=\frac{\sqrt{4a+2}}{a+1}$$

$$x=-\frac{\sqrt{4a+2}}{a+1}\text{, }a\geq -\frac{1}{2}$$