To solve the equation \( (x + 2)^2 - 49 = 0 \), follow these steps:

### Step 1: Isolate the squared term
Start by adding 49 to both sides of the equation:

\[
(x + 2)^2 = 49
\]

### Step 2: Take the square root of both sides
Next, take the square root of both sides to remove the square:

\[
x + 2 = \pm \sqrt{49}
\]

Since \( \sqrt{49} = 7 \), we have:

\[
x + 2 = \pm 7
\]

### Step 3: Solve for \( x \)
Now, solve for \( x \) by subtracting 2 from both sides for each case:

1. \( x + 2 = 7 \)
   \[
   x = 7 - 2 = 5
   \]

2. \( x + 2 = -7 \)
   \[
   x = -7 - 2 = -9
   \]

### Final Answer:
The solutions are \( x = 5 \) and \( x = -9 \).

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Would you like more details or have any questions? Here are some related problems you might find interesting:

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**Tip:** When dealing with squared terms, always consider both the positive and negative roots when taking the square root of both sides.

Learn how to solve the equation (x + 2)^2 - 49 = 0 step-by-step with detailed explanations and solutions. This problem involves quadratic equations and their applications, suitable for high school students.

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