Solve x^2-b^2=2ab

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

Solve for a (complex solution)

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

Steps for Solving Linear Equation

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

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

The equation is in standard form.

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

Divide both sides by 2b.

$$\frac{2ba}{2b}=\frac{\left(x-b\right)\left(x+b\right)}{2b}$$

Dividing by 2b undoes the multiplication by 2b.

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

Divide \left(x-b\right)\left(x+b\right) by 2b.

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

Solve for a

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

Steps for Solving Linear Equation

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

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

The equation is in standard form.

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

Divide both sides by 2b.

$$\frac{2ba}{2b}=\frac{\left(x-b\right)\left(x+b\right)}{2b}$$

Dividing by 2b undoes the multiplication by 2b.

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

Divide \left(x-b\right)\left(x+b\right) by 2b.

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

Solve for b

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

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