What is the maximum value of the expression `5-6x-x^(2)`

Answer

To find the maximum value of the expression \(5 - 6x - x^2\), we can follow these steps:

### Step 1: Identify the coefficients
The given expression is a quadratic equation in the standard form \(ax^2 + bx + c\). We can rewrite the expression as:
\[ -x^2 - 6x + 5 \]
Here, we can identify:
- \(a = -1\)
- \(b = -6\)
- \(c = 5\)

### Step 2: Use the formula for maximum value
For a quadratic equation \(ax^2 + bx + c\), the maximum or minimum value can be found using the formula:
\[ \text{Maximum/Minimum value} = c - \frac{b^2}{4a} \]
Since \(a\) is negative in this case, we will find the maximum value.

### Step 3: Substitute the values into the formula
Now, we substitute \(a\), \(b\), and \(c\) into the formula:
\[ \text{Maximum value} = 5 - \frac{(-6)^2}{4(-1)} \]

### Step 4: Calculate \(b^2\) and \(4a\)
First, calculate \(b^2\):
\[ (-6)^2 = 36 \]
Now calculate \(4a\):
\[ 4(-1) = -4 \]

### Step 5: Substitute and simplify
Now substitute these values back into the formula:
\[ \text{Maximum value} = 5 - \frac{36}{-4} \]
This simplifies to:
\[ \text{Maximum value} = 5 + 9 \]

### Step 6: Final calculation
Now, calculate the final result:
\[ \text{Maximum value} = 14 \]

### Conclusion
The maximum value of the expression \(5 - 6x - x^2\) is:
\[ \boxed{14} \]