https://file.aiquickdraw.com/mathbot/file/17290738049377fd500hz.jpg

The equation displayed in the image is:

\[
(x + 4)^2 = 9
\]

To solve this equation, follow these steps:

1. **Take the square root of both sides**:
   \[
   \sqrt{(x + 4)^2} = \pm \sqrt{9}
   \]
   This simplifies to:
   \[
   x + 4 = \pm 3
   \]

2. **Solve for \(x\)** by isolating \(x\):
   - Case 1: \(x + 4 = 3\)
     \[
     x = 3 - 4 = -1
     \]
   - Case 2: \(x + 4 = -3\)
     \[
     x = -3 - 4 = -7
     \]

Thus, the two solutions are \(x = -1\) and \(x = -7\).

Would you like more details or have any questions?

Here are five related questions:
1. How do we know when to take the square root of both sides of an equation?
2. What are other methods to solve quadratic equations besides factoring?
3. How would you graph this equation and its solutions?
4. What happens when the number under the square is negative?
5. Can this type of equation have complex solutions?

**Tip**: Always check both solutions by substituting them back into the original equation to ensure they satisfy it.

Learn how to solve the quadratic equation (x + 4)^2 = 9 by using the square root method. Detailed step-by-step solutions cover the process of isolating x and finding both possible answers. This problem is ideal for students in Grades 7-10.

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