To solve the equation \((x - 5)^2 = 16\), follow these steps:

### Step 1: Take the square root of both sides
\[
(x - 5) = \pm \sqrt{16}
\]
\[
(x - 5) = \pm 4
\]

### Step 2: Solve for \(x\) in both cases
1. \(x - 5 = 4\)
   \[
   x = 4 + 5 = 9
   \]
2. \(x - 5 = -4\)
   \[
   x = -4 + 5 = 1
   \]

### Final Answer:
The solutions are \(x = 9\) and \(x = 1\).

Would you like more details on any step, or have any questions?

Here are five related questions:
1. How would you solve \((x + 3)^2 = 25\)?
2. What are the steps for solving quadratic equations in general?
3. Can you explain the difference between solving linear and quadratic equations?
4. What happens when the square root involves complex numbers, like \((x - 5)^2 = -16\)?
5. How do you graph the function \((x - 5)^2 - 16 = 0\)?

**Tip**: Always remember that when solving square-root equations, both positive and negative roots need to be considered!

Explore the solution for the equation (x - 5)^2 = 16 with a clear, step-by-step guide. Learn how to apply the square root theorem and solve for x in two cases. Suitable for Grades 7-9 students studying quadratic equations and square roots.

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