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

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

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

Substituting these values into the quadratic formula:

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

Simplifying further:

\[
x = \frac{6 \pm \sqrt{36 + 64}}{2}
\]
\[
x = \frac{6 \pm \sqrt{100}}{2}
\]
\[
x = \frac{6 \pm 10}{2}
\]

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 or have any questions?

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Here are some related questions you might find interesting:

1. How do you derive the quadratic formula?
2. What does the discriminant tell you about the nature of the roots?
3. Can you solve this equation by completing the square?
4. How would you factor the quadratic equation \( x^2 - 6x - 16 = 0 \)?
5. What are the applications of quadratic equations in real-life situations?
6. How can you graph the quadratic function \( y = x^2 - 6x - 16 \)?
7. What is the axis of symmetry for the quadratic function \( y = x^2 - 6x - 16 \)?
8. How do you find the vertex of the quadratic function \( y = x^2 - 6x - 16 \)?

**Tip:** Always check the discriminant (\( b^2 - 4ac \)) before solving a quadratic equation to determine the nature of its roots.

Learn how to solve the quadratic equation x^2 - 6x - 16 = 0 step-by-step with detailed solutions. Understand the quadratic formula and its application in finding roots. Suitable for Grades 7-9.

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