To solve the quadratic equation \(9x^2 - x = 0\), follow these steps:

1. **Factor the equation**: 
   \[
   9x^2 - x = 0
   \]
   Factor out the common term \(x\):
   \[
   x(9x - 1) = 0
   \]

2. **Set each factor to zero**:
   \[
   x = 0 \quad \text{or} \quad 9x - 1 = 0
   \]

3. **Solve each equation**:
   - For \(x = 0\), this solution is already determined.
   - For \(9x - 1 = 0\), solve for \(x\):
     \[
     9x = 1
     \]
     \[
     x = \frac{1}{9}
     \]

So, the solutions to the equation \(9x^2 - x = 0\) are:
\[
x = 0 \quad \text{and} \quad x = \frac{1}{9}
\]

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

Here are 8 related questions that expand on this topic:

1. What is the general form of a quadratic equation?
2. How do you solve a quadratic equation using the quadratic formula?
3. What are the other methods for solving quadratic equations?
4. What does it mean to factor an equation?
5. Can all quadratic equations be factored easily?
6. What is the significance of the solutions to a quadratic equation?
7. How can you graph the solutions of a quadratic equation?
8. What are the applications of quadratic equations in real life?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy it.

Learn how to solve the quadratic equation 9x^2 - x = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring and solving quadratic equations. Suitable for students in Grades 7-9.

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