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

Question

Responses

x=8
x equals 8

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

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

x=−2

Answer 1

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

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

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

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

2. Now, substitute \( b \) and the discriminant into the quadratic formula:

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

3. Calculate the two possible values for \( x \):

First solution:

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

Second solution:

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

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
\( x \text{ equals } 8, x \text{ equals } -2 \)