Solve x^2-ab-a^2=bx

$${ x }^{ 2 } -ab- { a }^{ 2 } = bx$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=x-a\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=-a\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx from both sides.

$$x^{2}-ab-a^{2}-bx=0$$

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

$$-ab-a^{2}-bx=-x^{2}$$

Add a^{2} to both sides.

$$-ab-bx=-x^{2}+a^{2}$$

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by -a-x.

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

Dividing by -a-x undoes the multiplication by -a-x.

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

Divide \left(x+a\right)\left(-x+a\right) by -a-x.

$$b=x-a$$

Solve for b

$$\left\{\begin{matrix}\\b=x-a\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=-a\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract bx from both sides.

$$x^{2}-ab-a^{2}-bx=0$$

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

$$-ab-a^{2}-bx=-x^{2}$$

Add a^{2} to both sides.

$$-ab-bx=-x^{2}+a^{2}$$

Combine all terms containing b.

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

The equation is in standard form.

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

Divide both sides by -a-x.

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

Dividing by -a-x undoes the multiplication by -a-x.

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

Divide \left(x+a\right)\left(-x+a\right) by -a-x.

$$b=x-a$$

Solve for a

$$a=-x$$

$$a=x-b$$