Use the method of plugging In to solve the following problem.
If `(2x + 1)^2 = 100`, then which one of the following COULD equal x?

Options

A. `-11//2`
B. `-9//2`
C. `11/2`
D. `13//2`

Answer

To solve the equation \((2x + 1)^2 = 100\) using the method of plugging in, we will evaluate each option provided to find which value of \(x\) satisfies the equation.

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ (2x + 1)^2 = 100 \]

2. **Take the square root of both sides:**
\[ 2x + 1 = \pm 10 \]
This gives us two equations to solve:
\[ 2x + 1 = 10 \quad \text{and} \quad 2x + 1 = -10 \]

3. **Solve the first equation:**
\[ 2x + 1 = 10 \]
Subtract 1 from both sides:
\[ 2x = 9 \]
Divide by 2:
\[ x = \frac{9}{2} \]

4. **Solve the second equation:**
\[ 2x + 1 = -10 \]
Subtract 1 from both sides:
\[ 2x = -11 \]
Divide by 2:
\[ x = -\frac{11}{2} \]

5. **List the possible values of \(x\):**
The solutions we found are:
\[ x = \frac{9}{2} \quad \text{and} \quad x = -\frac{11}{2} \]

6. **Evaluate the options provided:**
- If \(x = -\frac{11}{2}\):
\[ 2\left(-\frac{11}{2}\right) + 1 = -11 + 1 = -10 \quad \Rightarrow \quad (-10)^2 = 100 \]
- If \(x = -\frac{9}{2}\):
\[ 2\left(-\frac{9}{2}\right) + 1 = -9 + 1 = -8 \quad \Rightarrow \quad (-8)^2 = 64 \]
- If \(x = \frac{11}{2}\):
\[ 2\left(\frac{11}{2}\right) + 1 = 11 + 1 = 12 \quad \Rightarrow \quad (12)^2 = 144 \]
- If \(x = \frac{13}{2}\):
\[ 2\left(\frac{13}{2}\right) + 1 = 13 + 1 = 14 \quad \Rightarrow \quad (14)^2 = 196 \]

7. **Conclusion:**
The only value of \(x\) that satisfies the original equation \((2x + 1)^2 = 100\) is:
\[ x = -\frac{11}{2} \]

### Final Answer:
The value of \(x\) that satisfies the equation is:
\[ \boxed{-\frac{11}{2}} \]