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To solve for \( x \) in the equation:

\[
x^2 - 3x - 18 = 0
\]

we can factor the quadratic expression. We are looking for two numbers that multiply to \(-18\) and add up to \(-3\).

1. The numbers that satisfy these conditions are \( -6 \) and \( 3 \), because:
   \[
   (-6) \times 3 = -18 \quad \text{and} \quad (-6) + 3 = -3
   \]

2. We can now rewrite the quadratic equation as:
   \[
   (x - 6)(x + 3) = 0
   \]

3. Using the zero-product property, set each factor equal to zero:
   \[
   x - 6 = 0 \quad \Rightarrow \quad x = 6
   \]
   \[
   x + 3 = 0 \quad \Rightarrow \quad x = -3
   \]

Therefore, the solutions are:
\[
x = 6, -3
\]

If you enter these values as "6, -3" in the answer box, it should be correct.

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

Here are five related questions to explore further:
1. How can the quadratic formula be used to solve \(x^2 - 3x - 18 = 0\)?
2. What other methods, besides factoring, can solve quadratic equations?
3. How do we identify if a quadratic equation has no real solutions?
4. What are the properties of the solutions of a quadratic equation in relation to its graph?
5. How would the solutions change if the equation were \(x^2 + 3x - 18 = 0\)?

**Tip:** Always check for factoring first when solving simple quadratic equations, as it's often the quickest method.

Solve for x in the equation x^2 - 3x - 18 = 0

Learn how to solve the quadratic equation x^2 - 3x - 18 = 0 using factoring. This step-by-step solution includes finding factors, applying the zero-product property, and solving for x. Perfect for students studying Algebra in Grade 9.

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