Solve the quadratic equation by finding the square roots.

(x+3)2=49
 
(Lowest solution) x=

(Highest solution) x=

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

1. **Take the square root of both sides**:
   \[
   x + 3 = \pm 7
   \]

2. **Split into two cases**:
   - **Case 1**: \(x + 3 = 7\)
   - **Case 2**: \(x + 3 = -7\)

3. **Solve each case**:
   - For Case 1:
     \[
     x + 3 = 7 \implies x = 7 - 3 = 4
     \]
   - For Case 2:
     \[
     x + 3 = -7 \implies x = -7 - 3 = -10
     \]

Thus, the solutions are:
- Lowest solution: \(x = -10\)
- Highest solution: \(x = 4\)

If you have any questions or need further details, let me know! Here are some related questions you might find interesting:

1. How can we graph the quadratic equation?
2. What are the implications of the solutions in the context of the equation?
3. How do you derive the quadratic formula from this type of equation?
4. Can you provide examples of real-world scenarios modeled by similar quadratic equations?
5. What methods can be used to solve quadratic equations besides completing the square?

**Tip**: Always check your solutions by substituting them back into the original equation!

Discover how to solve the quadratic equation (x+3)^2=49 by finding the square roots. This step-by-step guide reveals the lowest solution x=-10 and the highest solution x=4, essential for mastering algebra concepts. Suitable for students in Grades 7-9.

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