Question

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

Answer 1

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).