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To solve the equation \((u - 1)^2 - 9 = 0\), let's proceed step by step.

### Step 1: Rearrange the equation
\[
(u - 1)^2 - 9 = 0
\]
Add 9 to both sides:
\[
(u - 1)^2 = 9
\]

### Step 2: Take the square root of both sides
\[
u - 1 = \pm \sqrt{9}
\]
\[
u - 1 = \pm 3
\]

### Step 3: Solve for \( u \)
1. **Case 1:** \( u - 1 = 3 \)
   \[
   u = 3 + 1 = 4
   \]

2. **Case 2:** \( u - 1 = -3 \)
   \[
   u = -3 + 1 = -2
   \]

### Solution
The solutions are:
\[
u = 4, -2
\]

Would you like further details on any part of this solution, or do you have any other questions?

### Related Questions:
1. How do you solve quadratic equations by completing the square?
2. What is the process of isolating the variable in an equation?
3. How do you handle equations with square roots?
4. Can you solve \((x + 2)^2 - 16 = 0\) using the same method?
5. What are the general steps to solve equations of the form \((x - a)^2 - b = 0\)?

### Tip:
Always check your solutions by substituting them back into the original equation to verify they satisfy it.

Solve (u - 1)^2 - 9 = 0, where u is a real number. Simplify your answer as much as possible.

Learn how to solve the quadratic equation (u - 1)^2 - 9 = 0 with a step-by-step guide. Understand key algebra concepts like using the square root property to find the real values of u. Suitable for Grades 8-10 students.

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