Using the quadratic formula, find the solution to x2−6x−16=0

.(1 point)
Responses

x=−2
x equals negative 2

x=8
, x=−2
x equals 8 , x equals negative 2

x=8
, x=−8
x equals 8 , x equals negative 8

x=8

1 answer

To solve the quadratic equation \(x^2 - 6x - 16 = 0\) using the quadratic formula, we can use the formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

In this equation, \(a = 1\), \(b = -6\), and \(c = -16\).

Now, we can substitute these values into the formula.

  1. Calculate the discriminant (\(b^2 - 4ac\)): \[ b^2 - 4ac = (-6)^2 - 4(1)(-16) = 36 + 64 = 100 \]

  2. Substitute into the quadratic formula: \[ x = \frac{-(-6) \pm \sqrt{100}}{2(1)} = \frac{6 \pm 10}{2} \]

  3. This gives us two possible solutions:

    • For the positive solution: \[ x = \frac{6 + 10}{2} = \frac{16}{2} = 8 \]
    • For the negative solution: \[ x = \frac{6 - 10}{2} = \frac{-4}{2} = -2 \]

Thus, the solutions to the equation \(x^2 - 6x - 16 = 0\) are: \[ x = 8 \quad \text{and} \quad x = -2 \]

The correct response from your options would be: x=8, x=−2 (x equals 8, x equals negative 2).