To solve the equation \((x + 3)^2 = 49\), follow these steps:

### Step 1: Take the square root of both sides.
\[
\sqrt{(x + 3)^2} = \pm \sqrt{49}
\]
This simplifies to:
\[
x + 3 = \pm 7
\]

### Step 2: Solve for \( x \) by creating two cases.

#### Case 1: 
\[
x + 3 = 7
\]
Subtract 3 from both sides:
\[
x = 7 - 3 = 4
\]

#### Case 2: 
\[
x + 3 = -7
\]
Subtract 3 from both sides:
\[
x = -7 - 3 = -10
\]

### Final Answer:
The two possible solutions for \( x \) are:
\[
x = 4 \quad \text{or} \quad x = -10
\]

Would you like more details or further explanations?

Here are 5 related questions:
1. How do you solve \( (x - 5)^2 = 64 \)?
2. What happens if the equation was \( (x + 3)^2 = 48 \)?
3. How do you solve quadratic equations by factoring?
4. How can you solve a quadratic equation using the quadratic formula?
5. How do you complete the square to solve a quadratic equation?

**Tip:** Always remember to consider both the positive and negative square roots when solving equations like this one!

Learn how to solve the quadratic equation (x+3)^2 = 49 using square roots in this step-by-step guide. This problem involves key algebraic concepts, such as solving quadratic equations by taking square roots and handling two possible solutions. Suitable for students in Grades 8-10.

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