Completing the Square & the Quadratic Formula Quick Check

Question

3 of 53 of 5 Items
Question
Using the quadratic formula, find the solution to x2−6x−16=0.(1 point)
Responses

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

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

x=8
x equals 8

x=−2

Answer 1

To solve the equation \( x^2 - 6x - 16 = 0 \) using the quadratic formula, we start by identifying the coefficients \( a \), \( b \), and \( c \):

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

The quadratic formula is given by:

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

Now, plug in the values of \( a \), \( b \), and \( c \):

1. Calculate the discriminant:

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

2. Substitute into the quadratic formula:

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

3. Solve for the two possible values of \( x \):

• For the positive case:

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

• For the negative case:

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

Thus, the solutions are:

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

The correct response is:

x=8, x=−2 (or x equals 8, x equals negative 2)