Question
Of the strategies listed, which is most appropriate for solving \( (m+11)^{2}=64 \) ? What are the solutions? Enter your answers in the boxes. The square root property formula form The solutions are \( \square \) and \( \square \).
Ask by Ward Mccarthy. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The most appropriate strategy is the square root property. The solutions are \( m = -3 \) and \( m = -19 \).
Solution
The **square root property** is the most appropriate strategy for solving the equation \( (m + 11)^{2} = 64 \).
**Solving the equation:**
1. **Apply the square root property:**
\[
\sqrt{(m + 11)^{2}} = \sqrt{64}
\]
\[
m + 11 = \pm 8
\]
2. **Solve for \( m \) in both cases:**
- **Case 1:** \( m + 11 = 8 \)
\[
m = 8 - 11
\]
\[
m = -3
\]
- **Case 2:** \( m + 11 = -8 \)
\[
m = -8 - 11
\]
\[
m = -19
\]
**The solutions are \( \boxed{-3} \) and \( \boxed{-19} \).**
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To solve the equation \( (m+11)^{2}=64 \), we can use the square root property, which states that if \( x^2 = k \), then \( x = \pm \sqrt{k} \). Applying this, we take the square root of both sides: \( m + 11 = \pm 8 \). Now, let's break it down into two separate equations: 1. \( m + 11 = 8 \) leads to \( m = 8 - 11 = -3 \) 2. \( m + 11 = -8 \) leads to \( m = -8 - 11 = -19 \) The solutions are \( -3 \) and \( -19 \).