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

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 start with the standard form of a quadratic equation:

\[
ax^2 + bx + c = 0
\]

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

The quadratic formula is given by:

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

Let's compute the values step-by-step:

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

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

2. Now substituting back into the quadratic formula:

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

3. This gives us two potential solutions:

\[
x_1 = \frac{{6 + 10}}{2} = \frac{16}{2} = 8
\]

\[
x_2 = \frac{{6 - 10}}{2} = \frac{-4}{2} = -2
\]

Thus, the solutions to the equation \( x^2 - 6x - 16 = 0 \) are:

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

So, the correct response is:

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