A Shifted Square

When a squared bracket equals a negative, take the square root of both sides straight away. For (x - 2)^2 = -9 that gives x - 2 = 3i or x - 2 = -3i.

Each case is now a one-step equation: move the 2 across. So x = 2 + 3i or x = 2 - 3i, written with the real part first, as a + bi.

Why not expand first? Expanding gives x^2 - 4x + 4 = -9, a full quadratic, and you would have to complete the square all over again. The square is already complete, so the root goes straight to the answer. Check one: 2 + 3i - 2 is 3i, and (3i)^2 is -9.