Having some difficulty attempting this problem...

1) $\displaystyle (x-a)^{2} - b^{2} = 0$

Solving:

$\displaystyle (x-a)(x-a) - b^{2} = 0$

$\displaystyle x^{2} - ax - ax - a^{2} - b^{2} = 0$

$\displaystyle x^{2} - 2ax - a^{2} - b^{2} = 0$

... stuck.*

Completing the square

2) $\displaystyle x^{2} + 2bx + c = 0$

.... stuck