To solve the quadratic equation \( x^2 - 6x - 16 = 0 \) using the quadratic formula, we start with the formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
In your equation, we can identify \( a = 1 \), \( b = -6 \), and \( c = -16 \).
Now, calculate the discriminant \( b^2 - 4ac \):
\[ b^2 = (-6)^2 = 36 \] \[ 4ac = 4 \cdot 1 \cdot (-16) = -64 \] Thus, \[ b^2 - 4ac = 36 - (-64) = 36 + 64 = 100 \]
Now substitute \( a \), \( b \), and the discriminant into the quadratic formula:
\[ x = \frac{-(-6) \pm \sqrt{100}}{2 \cdot 1} \] \[ x = \frac{6 \pm 10}{2} \]
This results in two potential solutions:
\[ x = \frac{6 + 10}{2} = \frac{16}{2} = 8 \]
\[ x = \frac{6 - 10}{2} = \frac{-4}{2} = -2 \]
Therefore, the solutions are:
\[ x = 8 \quad \text{and} \quad x = -2 \]
The correct response among the options provided is:
x=8, x=−2 x equals 8, x equals negative 2
1 answer