Question

Using the quadratic formula, find the solution to x2−6x−16=0 .(1 point)
Responses

x=8
x equals 8

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

x=−2
x equals negative 2

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

Answer 1

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 \(x\):

1. \(x = \frac{6 + 10}{2} = \frac{16}{2} = 8\)
2. \(x = \frac{6 - 10}{2} = \frac{-4}{2} = -2\)

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**