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

x=−2
x equals negative 2

x=8

Answer 1

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

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

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

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

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

2. Use the quadratic formula:

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

3. Calculate the two possible values of \( x \):

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

So 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**
**x equals 8, x equals negative 2**