Question

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

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

x=−2
x equals negative 2

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

x=8
x equals 8

Answer 1

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:

1.
\[
x = \frac{6 + 10}{2} = \frac{16}{2} = 8
\]

2.
\[
x = \frac{6 - 10}{2} = \frac{-4}{2} = -2
\]

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**