To solve the quadratic equation $x^2 - 3x - 18 = 0$, follow these steps:

1. Identify the coefficients: The quadratic equation is in the form $ax^2 + bx + c = 0$, where: $a = 1, \quad b = -3, \quad c = -18$

2. Use the quadratic formula: The solutions of the quadratic equation are given by: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ Substituting the values $a = 1$, $b = -3$, and $c = -18$: $x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(-18)}}{2(1)}$ $x = \frac{3 \pm \sqrt{9 + 72}}{2}$ $x = \frac{3 \pm \sqrt{81}}{2}$

3. Simplify: $x = \frac{3 \pm 9}{2}$

   This gives two solutions: $x = \frac{3 + 9}{2} = 6 \quad \text{or} \quad x = \frac{3 - 9}{2} = -3$

Therefore, the solutions are: $\boxed{x = 6 \text{ or } x = -3}$

Would you like more details on any step or have any questions?

Related Questions

1. How do you complete the square to solve a quadratic equation?
2. What are the properties of quadratic functions and their graphs?
3. How do you find the vertex of the parabola represented by a quadratic equation?
4. What is the discriminant, and how does it determine the number of solutions?
5. How do you solve quadratic equations by factoring?

Tip: Always check the discriminant $b^2 - 4ac$ to determine if the quadratic equation has real, repeated, or complex solutions.