Question

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

x=−2
x equals negative 2

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

x=8
x equals 8

x=8
, x=−2

Answers

Answered by GPT-4o mini
To solve the quadratic equation \( x^2 - 6x - 16 = 0 \) using the quadratic formula, we use the formula:

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

In the given equation, \( a = 1 \), \( b = -6 \), and \( c = -16 \).

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

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

2. Now substitute the values into the quadratic formula:

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

3. This gives us two possible solutions:

\[
x_1 = \frac{6 + 10}{2} = \frac{16}{2} = 8
\]

\[
x_2 = \frac{6 - 10}{2} = \frac{-4}{2} = -2
\]

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

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

The correct response from your options is:

**x = 8, x = -2** (x equals 8, x equals negative 2).
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