12. Solve the equation $$ (x+3)^{2}=49 $$

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

1. **Take the Square Root of Both Sides:**
   
   $$
   \sqrt{(x + 3)^2} = \sqrt{49}
   $$
   
   This simplifies to:
   
   $$
   x + 3 = \pm 7
   $$
   
   The ± symbol indicates that there are two possible cases to consider.

2. **Solve for $$ x $$ in Each Case:**

- **Case 1:** $$ x + 3 = 7 $$
     
     $$
     x = 7 - 3
     $$
     
     $$
     x = 4
     $$
   
   - **Case 2:** $$ x + 3 = -7 $$
     
     $$
     x = -7 - 3
     $$
     
     $$
     x = -10
     $$

3. **Conclusion:**
   
   The equation $$ (x + 3)^2 = 49 $$ has two solutions:
   
   $$
   x = 4 \quad \text{and} \quad x = -10
   $$
The solutions are $$ x = 4 $$ and $$ x = -10 $$.

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