`n - sqrt(c +5)=1`
In the equation above, c is a constant. If `n =5,` what is the value of c ?

Options

A. `-1`
B. 0
C. 3
D. 11

Explanation

To solve the equation \( n - \sqrt{c + 5} = 1 \) for \( c \) when \( n = 5 \), we can follow these steps:

### Step-by-Step Solution:

1. **Substitute the value of \( n \)**:
Given that \( n = 5 \), we substitute this value into the equation:
\[ 5 - \sqrt{c + 5} = 1 \]

2. **Isolate the square root term**:
To isolate the square root, we can rearrange the equation:
\[ -\sqrt{c + 5} = 1 - 5 \]
Simplifying the right side:
\[ -\sqrt{c + 5} = -4 \]

3. **Remove the negative sign**:
Multiply both sides by -1:
\[ \sqrt{c + 5} = 4 \]

4. **Square both sides**:
To eliminate the square root, we square both sides of the equation:
\[ c + 5 = 4^2 \]
Simplifying the right side:
\[ c + 5 = 16 \]

5. **Solve for \( c \)**:
Now, we can solve for \( c \) by subtracting 5 from both sides:
\[ c = 16 - 5 \]
Thus, we find:
\[ c = 11 \]

### Final Answer:
The value of \( c \) is \( 11 \).

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