To solve the quadratic equation \(x^2 - 5x - 14 = 0\), we can use the quadratic formula:

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

Here, the coefficients are:
- \(a = 1\)
- \(b = -5\)
- \(c = -14\)

Let's substitute these values into the quadratic formula:

\[
x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(-14)}}{2(1)}
\]

Simplifying this:

\[
x = \frac{5 \pm \sqrt{25 + 56}}{2}
\]

\[
x = \frac{5 \pm \sqrt{81}}{2}
\]

\[
x = \frac{5 \pm 9}{2}
\]

This gives us two possible solutions:

\[
x_1 = \frac{5 + 9}{2} = \frac{14}{2} = 7
\]

\[
x_2 = \frac{5 - 9}{2} = \frac{-4}{2} = -2
\]

So, the solutions to the equation \(x^2 - 5x - 14 = 0\) are:

\[
x = 7 \quad \text{or} \quad x = -2
\]

Would you like further details or have any questions?

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Here are some related questions:

1. How do you factorize a quadratic equation?
2. What are the properties of the discriminant in a quadratic equation?
3. How do you complete the square to solve a quadratic equation?
4. What are the applications of quadratic equations in real life?
5. How can you derive the quadratic formula?
6. What is the significance of the vertex of a quadratic function?
7. Can all quadratic equations be solved by factoring?
8. How do you graph a quadratic equation?

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

Learn how to solve the quadratic equation x² - 5x - 14 with a step-by-step solution using the quadratic formula. Understand the coefficients and how to determine the solutions. Suitable for high school students.

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