Solve x^2+2ax+a-2=0

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

Solve for a

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

$$x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Add 2 to both sides.

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

Combine all terms containing a.

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

The equation is in standard form.

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

Divide both sides by 2x+1.

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

Dividing by 2x+1 undoes the multiplication by 2x+1.

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

Solve for x

$$x=\sqrt{a^{2}-a+2}-a$$

$$x=-\sqrt{a^{2}-a+2}-a$$