Question

using a quadratic formula, find the solution to x^2 - 6x - 16 = 0
a x = -2
b x = 8, x = -8
c x = 8
d x = 8, x = -2

Answer 1

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

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

In this equation, \(a\), \(b\), and \(c\) are the coefficients from the quadratic equation \(ax^2 + bx + c = 0\). For the given equation:

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

Now we will calculate \(b^2 - 4ac\):

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

Next, we can plug everything into the quadratic formula:

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

This simplifies to:

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

Now, calculating the two possible values for \(x\):

1. Using the positive root:
\[
x = \frac{{6 + 10}}{2} = \frac{16}{2} = 8
\]

2. Using the negative root:
\[
x = \frac{{6 - 10}}{2} = \frac{-4}{2} = -2
\]

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

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

Thus, the correct answer is \(d\) \(x = 8, x = -2\).