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

1. **Factor the equation:**

   The equation can be factored by taking out the common factor \(x\):

   \[
   x(9x + 1) = 0
   \]

2. **Set each factor equal to zero:**

   For the product to be zero, at least one of the factors must be zero. Therefore, set each factor equal to zero:

   \[
   x = 0
   \]
   \[
   9x + 1 = 0
   \]

3. **Solve for \(x\) in each equation:**

   - From the first factor:
     \[
     x = 0
     \]

   - From the second factor:
     \[
     9x + 1 = 0
     \]
     Subtract 1 from both sides:
     \[
     9x = -1
     \]
     Divide both sides by 9:
     \[
     x = -\frac{1}{9}
     \]

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

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How do you factor more complex quadratic equations?
2. What is the quadratic formula, and how can it be used to solve any quadratic equation?
3. How can you graph the solutions of a quadratic equation on a coordinate plane?
4. What are the roots of a quadratic equation, and how are they related to the solutions?
5. How does the discriminant of a quadratic equation determine the nature of its solutions?

**Tip:** When factoring quadratic equations, always look for a common factor before trying other methods like the quadratic formula or completing the square.

Learn how to solve the quadratic equation 9x² + x = 0 by factoring. This step-by-step solution covers factoring techniques and the zero product property. Suitable for students in Grades 8-10.

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