Solve (x-a)^2=(x-b)

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

Solve for b

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

Steps for Solving Linear Equation

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(x-a\right)^{2}.

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

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

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

Subtract x from both sides.

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

The equation is in standard form.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide -x+\left(x-a\right)^{2} by -1.

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

Solve for a (complex solution)

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

$$a=x-\sqrt{x-b}$$

Solve for a

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

$$a=x-\sqrt{x-b}\text{, }x\geq b$$