The expression \( x^2 - x - 30 \) is a quadratic expression. To solve it, we can factor it as follows:

### Step 1: Set the equation to zero
To solve for \( x \), set the expression equal to zero:
\[
x^2 - x - 30 = 0
\]

### Step 2: Factor the expression
We need to find two numbers that multiply to \(-30\) and add up to \(-1\). The numbers that satisfy this condition are \( -6 \) and \( 5 \), because:
\[
-6 \times 5 = -30 \quad \text{and} \quad -6 + 5 = -1
\]

### Step 3: Write the factors
Now we can factor the expression as:
\[
(x - 6)(x + 5) = 0
\]

### Step 4: Solve for \( x \)
Set each factor equal to zero and solve for \( x \):
1. \( x - 6 = 0 \Rightarrow x = 6 \)
2. \( x + 5 = 0 \Rightarrow x = -5 \)

### Final Answer
The solutions to the equation \( x^2 - x - 30 = 0 \) are:
\[
x = 6 \quad \text{and} \quad x = -5
\]

Would you like a more detailed explanation or have any other questions?

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Here are five related questions:
1. How do we determine the factors for other quadratic equations like \(x^2 - 2x - 35\)?
2. What is the quadratic formula, and how can it be used if factoring is difficult?
3. How does completing the square work for solving quadratic equations?
4. What is the difference between the roots and factors of a quadratic equation?
5. Can this equation be graphed, and if so, where do the solutions appear on the graph?

**Tip:** To quickly check if your factors are correct, multiply them to see if they return the original quadratic expression.

Discover a step-by-step solution to the quadratic equation x^2 - x - 30. Learn key algebraic concepts, including factoring and using the zero product property, to find solutions to x^2 - x - 30 = 0. Suitable for Grades 8-10.

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