Solve the equation (x−1)2 − 25 = 0 for x.

$$(x-1)^2 - 25 = 0$$ $$(x-1)^2 = 25$$

Remember to consider both the positive and negative roots.

$$\sqrt{(x-1)^2} = \pm\sqrt{25}$$ $$x-1 = \pm 5$$

Case 1: Using the positive root

$$x-1 = 5$$ $$x = 5 + 1$$ $$x = 6$$

Case 2: Using the negative root

$$x-1 = -5$$ $$x = -5 + 1$$ $$x = -4$$

The solutions for $x$ are 6 and $-4$.

$$x = 6, x = -4$$