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=−2
x equals 8 , x equals negative 2

x=8, x=−8

Answer 1

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

The quadratic formula is given by:

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

In the equation \( x^2 - 6x - 16 = 0 \), the coefficients are:
- \( a = 1 \)
- \( b = -6 \)
- \( c = -16 \)

Now we calculate the discriminant \( b^2 - 4ac \):

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

Now we can apply the quadratic formula:

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

This gives us two solutions:

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 \( x = 8 \) and \( x = -2 \).

So the correct response is:

**x=8, x=−2**