Question

Solve the equation by the square root property.
3​(xplus3​)squaredequals36
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Part 1
The solution set is StartSet nothing EndSet . nbsp

Answer 1

To solve the equation \( 3(x + 3)^2 = 36 \) using the square root property, we first isolate the squared term. Here are the steps:

1. **Divide both sides by 3:**
\[
(x + 3)^2 = \frac{36}{3}
\]
\[
(x + 3)^2 = 12
\]

2. **Apply the square root property:**
Taking the square root of both sides gives us:
\[
x + 3 = \pm \sqrt{12}
\]

3. **Simplify \(\sqrt{12}\):**
We can simplify \(\sqrt{12}\):
\[
\sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3}
\]
Thus, the equation becomes:
\[
x + 3 = \pm 2\sqrt{3}
\]

4. **Solve for \(x\):**
Now, we can split this into two cases:
- Case 1: \( x + 3 = 2\sqrt{3} \)
- Case 2: \( x + 3 = -2\sqrt{3} \)

Solving these cases gives:
- For Case 1:
\[
x = 2\sqrt{3} - 3
\]

- For Case 2:
\[
x = -2\sqrt{3} - 3
\]

5. **Final solution set:**
Therefore, the solution set is:
\[
\{ 2\sqrt{3} - 3, -2\sqrt{3} - 3 \}
\]

So, the complete solution set is:
\[
\{ 2\sqrt{3} - 3, -2\sqrt{3} - 3 \}
\]