Using the quadratic formula, find the solution to x^2−6x−16=0

Question

.(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.