Solve y=x^2+2ax+2

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

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{x^{2}-y+2}{2x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=2\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+2ax+2=y$$

Subtract x^{2} from both sides.

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

Subtract 2 from both sides.

$$2ax=y-x^{2}-2$$

The equation is in standard form.

$$2xa=-x^{2}+y-2$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{-x^{2}+y-2}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

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

Solve for a

$$\left\{\begin{matrix}a=-\frac{x^{2}-y+2}{2x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=2\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+2ax+2=y$$

Subtract x^{2} from both sides.

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

Subtract 2 from both sides.

$$2ax=y-x^{2}-2$$

The equation is in standard form.

$$2xa=-x^{2}+y-2$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{-x^{2}+y-2}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

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

Solve for x (complex solution)

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

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

Solve for x

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

$$x=-\sqrt{y+a^{2}-2}-a\text{, }y\geq 2-a^{2}$$