Let's solve the equation \((x+3)^2 - 225 = 0\).

### Step 1: Isolate the squared term
Add 225 to both sides of the equation:
\[
(x+3)^2 = 225
\]

### Step 2: Take the square root of both sides
To remove the square, take the square root of both sides:
\[
x+3 = \pm 15
\]

### Step 3: Solve for \(x\)
Now, solve for \(x\) by subtracting 3 from both sides for each case:
1. \(x + 3 = 15 \Rightarrow x = 15 - 3 = 12\)
2. \(x + 3 = -15 \Rightarrow x = -15 - 3 = -18\)

### Solution:
The solutions are:
\[
x = 12 \quad \text{or} \quad x = -18
\]

Would you like a more detailed explanation on any of the steps?

Here are 5 related questions to deepen your understanding:
1. How do you factor a quadratic expression like \((x+3)^2 - 225\)?
2. What happens if the equation had been \((x+3)^2 + 225 = 0\)?
3. How do you graph the equation \((x+3)^2 - 225 = 0\)?
4. Can you solve \((x-5)^2 = 49\)?
5. What are the real-life applications of solving quadratic equations?

**Tip**: Always remember to consider both the positive and negative square roots when solving equations involving squares.

Learn how to solve the quadratic equation (x+3)² - 225 = 0 with a step-by-step explanation. This guide covers key concepts such as isolating squared terms and applying square roots, suitable for Grades 8-10 students.

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