A Shifted Square

When a squared bracket equals a negative, take the square root of both sides straight away. For ${\left(x-2\right)}^{2} = -9$ 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 ${\left(3i\right)}^{2}$ is -9.