1. **State the problem:** Solve the equation $$(x - 1)^2 = 3$$ for $x$. 2. **Recall the formula:** To solve equations of the form $$(x - a)^2 = b$$, take the square root of both sides: $$x - a = \pm \sqrt{b}$$ 3. **Apply the formula:** Here, $a = 1$ and $b = 3$, so $$x - 1 = \pm \sqrt{3}$$ 4. **Solve for $x$:** $$x = 1 \pm \sqrt{3}$$ 5. **Final answer:** $$x = 1 + \sqrt{3} \quad \text{or} \quad x = 1 - \sqrt{3}$$ This means the solutions are two values symmetric around 1, separated by the distance $\sqrt{3}$.