To solve the equation \( (x + 6)^2 = 64 \), follow these steps:

### Step 1: Take the square root of both sides.
First, apply the square root to both sides of the equation:

\[
\sqrt{(x + 6)^2} = \pm \sqrt{64}
\]

This simplifies to:

\[
x + 6 = \pm 8
\]

### Step 2: Solve for \(x\).
Now, solve for \(x\) by separating the equation into two cases:

1. \( x + 6 = 8 \)
   \[
   x = 8 - 6
   \]
   \[
   x = 2
   \]

2. \( x + 6 = -8 \)
   \[
   x = -8 - 6
   \]
   \[
   x = -14
   \]

### Final Answer:
The two solutions are:
\[
x = 2 \quad \text{or} \quad x = -14
\]

Would you like more details on this solution, or do you have any further questions?

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Here are 5 related questions to practice:
1. Solve \( (x - 4)^2 = 49 \).
2. Solve \( (x + 3)^2 = 25 \).
3. Solve \( (2x + 5)^2 = 36 \).
4. Solve \( (x + 7)^2 = 81 \).
5. Solve \( (x - 1)^2 = 100 \).

**Tip:** Remember to consider both the positive and negative roots when taking square roots!

Learn how to solve the quadratic equation (x+6)^2 = 64 with a clear step-by-step solution. This problem involves using square roots and solving for x, making it ideal for students in Grades 8-10.

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