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

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

Here, the coefficients are:
- \(a = 1\)
- \(b = -6\)
- \(c = -16\)

Now, let's plug these values into the quadratic formula:

\[
x = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(1)(-16)}}{2(1)}
\]

Simplifying this:

\[
x = \frac{6 \pm \sqrt{36 + 64}}{2}
\]

\[
x = \frac{6 \pm \sqrt{100}}{2}
\]

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

This gives us two possible solutions:

\[
x_1 = \frac{6 + 10}{2} = \frac{16}{2} = 8
\]

\[
x_2 = \frac{6 - 10}{2} = \frac{-4}{2} = -2
\]

So, the solutions are \(x = 8\) and \(x = -2\).

Would you like more details on this solution, or do you have any questions?

Here are 8 related questions to explore further:

1. How do you determine the discriminant in a quadratic equation?
2. What does the discriminant tell you about the nature of the roots?
3. Can you solve a quadratic equation by completing the square?
4. What is the significance of the vertex form of a quadratic equation?
5. How do you factor a quadratic equation?
6. What are the roots of the equation \(x^2 + 4x + 4 = 0\)?
7. How does the quadratic formula relate to the graph of a parabola?
8. Can quadratic equations have complex roots?

**Tip:** Always double-check your discriminant (\(b^2 - 4ac\)) to understand the nature of the solutions (real or complex) before solving the equation.

Learn how to solve the quadratic equation x^2 - 6x - 16 = 0 with detailed step-by-step solutions. Understand the application of the quadratic formula and determine the roots of the equation. Suitable for high school students studying algebra.

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