To solve the quadratic equation \( x^2 - 6x - 16 = 0 \) using the quadratic formula, we start by identifying the coefficients:
\[ a = 1, \quad b = -6, \quad c = -16 \]
The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Now we will calculate \( b^2 - 4ac \):
\[ b^2 - 4ac = (-6)^2 - 4 \cdot 1 \cdot (-16) = 36 + 64 = 100 \]
Now we can apply the quadratic formula:
\[ x = \frac{-(-6) \pm \sqrt{100}}{2 \cdot 1} = \frac{6 \pm 10}{2} \]
This gives us two possible solutions:
- When using the plus sign:
\[ x = \frac{6 + 10}{2} = \frac{16}{2} = 8 \]
- When using the minus sign:
\[ x = \frac{6 - 10}{2} = \frac{-4}{2} = -2 \]
Thus, the solutions to the equation \( x^2 - 6x - 16 = 0 \) are:
\[ x = 8 \quad \text{and} \quad x = -2 \]
The correct response is:
x = 8, x = -2 (or in another format, x equals 8, x equals negative 2).