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

Question

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 start by identifying the coefficients:

• \(a = 1\)
• \(b = -6\)
• \(c = -16\)

The quadratic formula is given by:

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

First, we calculate the discriminant (\(b^2 - 4ac\)):

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

Now, compute the discriminant:

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

Now we can substitute back into the quadratic formula:

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

Now, we solve for the two possible values of \(x\):

1. For \(6 + 10\):

\[ x = \frac{16}{2} = 8 \]

2. For \(6 - 10\):

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

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

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

Among the given responses, the correct one is:

x=8, x=−2 (or x equals 8, x equals negative 2)