Solve x^2+2ax+b^2=0

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

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

Subtract b^{2} from both sides.

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

The equation is in standard form.

$$2xa=-x^{2}-b^{2}$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{-x^{2}-b^{2}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{-x^{2}-b^{2}}{2x}$$

Divide -x^{2}-b^{2} by 2x.

$$a=-\frac{b^{2}}{2x}-\frac{x}{2}$$

Solve for a

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

Steps for Solving Linear Equation

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

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

Subtract b^{2} from both sides.

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

The equation is in standard form.

$$2xa=-x^{2}-b^{2}$$

Divide both sides by 2x.

$$\frac{2xa}{2x}=\frac{-x^{2}-b^{2}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$a=\frac{-x^{2}-b^{2}}{2x}$$

Divide -x^{2}-b^{2} by 2x.

$$a=-\frac{b^{2}}{2x}-\frac{x}{2}$$

Solve for b (complex solution)

$$b=-i\sqrt{x}\sqrt{x+2a}$$

$$b=i\sqrt{x}\sqrt{x+2a}$$

Solve for b

$$b=\sqrt{-x\left(x+2a\right)}$$

$$b=-\sqrt{-x\left(x+2a\right)}\text{, }\left(x\geq 0\text{ or }x\geq -2a\right)\text{ and }\left(x\leq 0\text{ or }x\leq -2a\right)$$