The equation you've provided is:

$(x - 5)^2 + 4 = 0$

To solve for $x$, let's follow these steps:

Step 1: Subtract 4 from both sides of the equation:

$(x - 5)^2 = -4$

Step 2: Take the square root of both sides:

$x - 5 = \pm \sqrt{-4}$ Since $\sqrt{-4}$ involves an imaginary number, we express it as $2i$ (where $i$ is the imaginary unit).

$x - 5 = \pm 2i$

Step 3: Solve for $x$:

$x = 5 \pm 2i$

Thus, the solutions are:

$x = 5 + 2i \quad \text{or} \quad x = 5 - 2i$

The equation has two complex solutions: $x = 5 + 2i$ and $x = 5 - 2i$.

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. How do you solve quadratic equations involving imaginary numbers?
2. What is the square root of other negative numbers?
3. Can a quadratic equation have purely real solutions?
4. How do you simplify expressions with complex numbers?
5. What does $i$ represent in mathematics?

Tip: Imaginary numbers arise when you take the square root of a negative number. The imaginary unit $i$ is defined as $\sqrt{-1}$.