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 equals 8

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

x=8, x=−2

Answer 1

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

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

Here, \( a = 1 \), \( b = -6 \), and \( c = -16 \).

1. Calculate the discriminant \( b^2 - 4ac \):

\[
b^2 = (-6)^2 = 36
\]
\[
4ac = 4 \times 1 \times (-16) = -64
\]
\[
b^2 - 4ac = 36 - (-64) = 36 + 64 = 100
\]

2. Now, substitute into the quadratic formula:

\[
x = \frac{-(-6) \pm \sqrt{100}}{2 \times 1}
\]
\[
x = \frac{6 \pm 10}{2}
\]

3. Calculate the two potential values for \( x \):

\[
x_1 = \frac{6 + 10}{2} = \frac{16}{2} = 8
\]
\[
x_2 = \frac{6 - 10}{2} = \frac{-4}{2} = -2
\]

Thus, the solutions to the equation \( x^2 - 6x - 16 = 0 \) are:

\[
x = 8 \quad \text{and} \quad x = -2
\]

The correct response is:

**x=8, x=−2**.