Solve (x-a)^2=b

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

Solve for b

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

Solution Steps

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

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

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

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

Solve for a (complex solution)

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

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

Solve for a

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

$$a=x-\sqrt{b}\text{, }b\geq 0$$