To solve the quadratic equation \( x^2 - 3x - 18 = 0 \) by factoring, follow these steps:

### Step 1: Identify the coefficients
The given equation is in the standard quadratic form \( ax^2 + bx + c = 0 \), where:
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = -3 \) (coefficient of \( x \))
- \( c = -18 \) (constant term)

### Step 2: Find two numbers that multiply to \( ac \) and add to \( b \)
- Multiply \( a \) and \( c \): \( 1 \times (-18) = -18 \).
- We need two numbers that multiply to \(-18\) and add to \(-3\).

The two numbers that work are \( -6 \) and \( 3 \), because:
- \( -6 \times 3 = -18 \)
- \( -6 + 3 = -3 \)

### Step 3: Write the middle term as a sum of two terms
Rewrite the equation by breaking the middle term \( -3x \) into \( -6x + 3x \):
\[
x^2 - 6x + 3x - 18 = 0
\]

### Step 4: Factor by grouping
Group the terms in pairs:
\[
(x^2 - 6x) + (3x - 18) = 0
\]
Factor out the greatest common factor from each group:
\[
x(x - 6) + 3(x - 6) = 0
\]

### Step 5: Factor out the common binomial
\[
(x - 6)(x + 3) = 0
\]

### Step 6: Solve for \( x \)
Set each factor equal to zero and solve for \( x \):
\[
x - 6 = 0 \quad \text{or} \quad x + 3 = 0
\]
\[
x = 6 \quad \text{or} \quad x = -3
\]

### Final Answer
The solutions are \( x = 6 \) and \( x = -3 \).

Would you like more details or have any questions about the process?

Here are 5 related questions:
1. How do you factor quadratic equations with a leading coefficient other than 1?
2. What is the difference between factoring and using the quadratic formula?
3. How can you check if the solutions to a quadratic equation are correct?
4. What do you do if a quadratic equation cannot be factored?
5. How do you factor a perfect square trinomial?

**Tip:** Always check your solutions by substituting them back into the original equation.

Discover how to solve the quadratic equation x²-3x-18=0 by factoring. This detailed guide covers factoring techniques and the zero product property, perfect for students in Grades 8-10. Learn step-by-step to master quadratic equations.

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