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