Solve a^2x+x-a=0

$$a ^ { 2 } x + x - a = 0$$

Solve for x (complex solution)

$$x=\frac{a}{a^{2}+1}$$

$$a\neq -i\text{ and }a\neq i$$

Steps for Solving Linear Equation

Add a to both sides. Anything plus zero gives itself.

$$a^{2}x+x=a$$

Combine all terms containing x.

$$\left(a^{2}+1\right)x=a$$

Divide both sides by a^{2}+1.

$$\frac{\left(a^{2}+1\right)x}{a^{2}+1}=\frac{a}{a^{2}+1}$$

Dividing by a^{2}+1 undoes the multiplication by a^{2}+1.

$$x=\frac{a}{a^{2}+1}$$

Solve for x

$$x=\frac{a}{a^{2}+1}$$

Steps for Solving Linear Equation

Add a to both sides. Anything plus zero gives itself.

$$a^{2}x+x=a$$

Combine all terms containing x.

$$\left(a^{2}+1\right)x=a$$

Divide both sides by a^{2}+1.

$$\frac{\left(a^{2}+1\right)x}{a^{2}+1}=\frac{a}{a^{2}+1}$$

Dividing by a^{2}+1 undoes the multiplication by a^{2}+1.

$$x=\frac{a}{a^{2}+1}$$

Solve for a (complex solution)

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

Solve for a

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