Solve ax^2+a-2=0

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

Solve for a (complex solution)

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

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

Steps for Solving Linear Equation

Add 2 to both sides. Anything plus zero gives itself.

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

Combine all terms containing a.

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

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

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

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

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

Solve for a

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

Steps for Solving Linear Equation

Add 2 to both sides. Anything plus zero gives itself.

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

Combine all terms containing a.

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

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

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

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

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

Solve for x (complex solution)

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

$$x=\sqrt{-1+\frac{2}{a}}\text{, }a\neq 0$$

Solve for x

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

$$x=-\sqrt{-1+\frac{2}{a}}\text{, }a>0\text{ and }a\leq 2$$