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.

Learn how to solve the quadratic equation x^2 - 3x - 18 step by step using the quadratic formula. This problem covers key algebraic concepts, including identifying coefficients and applying the quadratic formula. Suitable for students in Grades 7-9.

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