Question

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

x=−2

x=8, x=−8

x=8

x=8, x=−2

Answer 1

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

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

In this case, the coefficients are:
- \( a = 1 \)
- \( b = -6 \)
- \( c = -16 \)

Now, we can plug these values into the formula:

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

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

3. This results in two potential solutions:
- For the plus sign:
\[
x = \frac{6 + 10}{2} = \frac{16}{2} = 8
\]

- For the minus sign:
\[
x = \frac{6 - 10}{2} = \frac{-4}{2} = -2
\]

Thus, the solutions are \( x = 8 \) and \( x = -2 \).

The correct response is **x=8, x=−2**.