Question

Using the quadratic formula, find the solution to x2−6x−16=0 .(1 point) Responses x=8 , x=−8 x equals 8 , x equals negative 8 x=−2 x equals negative 2 x=8 x equals 8 x=8 , x=−2

Answer 1

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

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

where \(a = 1\), \(b = -6\), and \(c = -16\).

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. **Substitute the values into the formula**:

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

3. **Calculate the two possible values for x**:

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

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

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

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

The correct response is: **x = 8, x = -2**.