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Question

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

x=−2
x equals negative 2

x=8
x equals 8

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

x=8, x=−8

Answer 1

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

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

where \( a = 1 \), \( b = -6 \), and \( c = -16 \).

1. Calculate \( b^2 - 4ac \):

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

2. Substitute values into the formula:

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

3. Calculate the two possible solutions:

   For the positive root:

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

   For the negative root:

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

So the solutions to the equation \( x^2 - 6x - 16 = 0 \) are \( x = 8 \) and \( x = -2 \).

The correct response is:

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