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 \(\sqrt{-1}\).

Learn how to solve the quadratic equation (x - 5)^2 + 4 = 0, which involves imaginary numbers. This step-by-step solution covers key algebra concepts like complex numbers and properties of square roots, making it suitable for students in Grades 10-12.

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