Question

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

x=8
x equals 8

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

x=−2
x equals negative 2

x=8
, x=−2

Answer 1

To solve the quadratic equation \(x^2 - 6x - 16 = 0\) using the quadratic formula, we first recall that the quadratic formula is given by:

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

For the equation \(x^2 - 6x - 16 = 0\), we identify the coefficients:

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

Now, we can calculate the values needed for the quadratic formula.

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

2. Now substitute into the quadratic formula:
\[
x = \frac{-(-6) \pm \sqrt{100}}{2 \cdot 1} = \frac{6 \pm 10}{2}
\]

3. This gives us two potential solutions:
- For the positive case:
\[
x = \frac{6 + 10}{2} = \frac{16}{2} = 8
\]
- For the negative case:
\[
x = \frac{6 - 10}{2} = \frac{-4}{2} = -2
\]

Thus, the solutions to the equation \(x^2 - 6x - 16 = 0\) are:
\[
x = 8 \quad \text{and} \quad x = -2
\]

From the provided responses, the correct one is:
**x=8, x=−2**.