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

Question

Responses

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

x=8
x equals 8

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

x=−2
x equals negative 2

Answer 1

To solve the quadratic equation \(x^2 - 6x - 16 = 0\) using the quadratic formula, we start with the standard form of a quadratic equation:

\[ ax^2 + bx + c = 0 \]

In this case, \(a = 1\), \(b = -6\), and \(c = -16\).

The quadratic formula is given by:

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

Now, we calculate the discriminant:

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

Since the discriminant is \(100\), we can calculate the roots:

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

This gives us two solutions:

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

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

\[ x = 8, \quad x = -2 \]

The correct response is:

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