Epsilon Delta as x approaches a variable

Question

I'm having some trouble figuring out how to solve the following epsilon delta problem:

Limit of $(x-2)^2$ as $x$ approaches $b$.

I can find $(x+b-4)(x-b) < \epsilon$, but I'm not sure where to go from there.

Answer 1

$|(x+b-4)(x-b)| \leq (|x-b|+|2b-4|)|x-b| <(\delta+|2b-4|)\delta <\epsilon $ if $\delta <1$ and $\delta <\frac {\epsilon} {(1+|2b-4|)}$.