Question

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

Answer 1

To find the solutions to the quadratic equation \(x^2 - 6x - 16 = 0\) using the quadratic formula, we can start by identifying the coefficients in the standard form \(ax^2 + bx + c = 0\):

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

The quadratic formula is given by:

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

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

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

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

2. Now apply the quadratic formula:

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

Simplifying this gives:

\[
x = \frac{{6 \pm 10}}{2}
\]

Now we have two potential 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:

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