Question

Using the quadratic formula, find the solution to x^2−6x−16=0
.(1 point)
Responses

x=8

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

Answer 1

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

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

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

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

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

Now, we take the square root of the discriminant:

\[
\sqrt{100} = 10
\]

Now we can plug this back into the quadratic formula:

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

This gives us two possible solutions 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 are:

\[
x = 8, \quad x = -2
\]

The correct response is:

**x equals 8, x equals negative 2**.