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