Using the quadratic formula, find the solution to x2−6x−16=0

Question

.(1 point)
Responses

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

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

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 first identify 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, plug in the values of \( a \), \( b \), and \( c \):

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

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

2. Take the square root of the discriminant:

\[ \sqrt{100} = 10 \]

3. Plug the values into the quadratic formula:

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

This results in two solutions:

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

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

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

\[ x = 8 \quad \text{and} \quad x = -2 \]

So the correct response is:

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