To solve the quadratic equation \(x^2 - 6x - 16 = 0\) using the quadratic formula, we can use:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
where \(a = 1\), \(b = -6\), and \(c = -16\).
First, we calculate the discriminant:
\[ b^2 - 4ac = (-6)^2 - 4 \cdot 1 \cdot (-16) = 36 + 64 = 100 \]
Next, we substitute the values into the quadratic formula:
\[ x = \frac{-(-6) \pm \sqrt{100}}{2 \cdot 1} = \frac{6 \pm 10}{2} \]
Now we compute the two possible values for \(x\):
- \(x = \frac{6 + 10}{2} = \frac{16}{2} = 8\)
- \(x = \frac{6 - 10}{2} = \frac{-4}{2} = -2\)
Thus, the solutions to the equation are:
\[ x = 8 \quad \text{and} \quad x = -2 \]
The correct response is:
x = 8, x = −2
x equals 8 , x equals negative 2