Question

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

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

x=−2
x equals negative 2

x=8
x equals 8

x=8
, x=−8

Answer 1

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

\[
a = 1, \quad b = -6, \quad c = -16
\]

The quadratic formula is given by:

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

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

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

Now we can apply the quadratic formula:

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

This gives us two possible solutions:

1. When using the plus sign:

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

2. When using the minus sign:

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

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** (or in another format, x equals 8, x equals negative 2).