Using the quadratic formula, find the solution to x2−6x−16=0

Question

𝑥
2
−
6
𝑥
−
16
=
0
.(1 point)
Responses

x=−2
𝑥
=
−
2
x equals negative 2

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

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

x=8

Answer 1

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

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

where \(a\), \(b\), and \(c\) are the coefficients from the equation in the form \(ax^2 + bx + c = 0\).

In this case:

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

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

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

Now we can substitute the values into the quadratic formula:

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

This gives us two potential solutions:

1. \(x = \frac{6 + 10}{2} = \frac{16}{2} = 8\)
2. \(x = \frac{6 - 10}{2} = \frac{-4}{2} = -2\)

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

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