The equation you've provided is:

\[
2b^2 = 9b
\]

### Step-by-step solution:

1. First, let's rearrange the equation so that one side is equal to zero:
   \[
   2b^2 - 9b = 0
   \]

2. Now, factor the left-hand side:
   \[
   b(2b - 9) = 0
   \]

3. To solve for \(b\), we set each factor equal to zero:

   - \(b = 0\)
   - \(2b - 9 = 0\)

4. Solving \(2b - 9 = 0\) for \(b\):
   \[
   2b = 9
   \]
   \[
   b = \frac{9}{2}
   \]

### Final answer:
The solutions are:
\[
b = 0 \quad \text{or} \quad b = \frac{9}{2}
\]

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

Here are 5 related questions:
1. How do you factor quadratic equations in general?
2. What does it mean for an equation to have multiple solutions?
3. Can you explain how to complete the square for quadratic equations?
4. How can we graph quadratic functions and interpret their solutions?
5. What are the real-world applications of solving quadratic equations?

**Tip:** Always check for common factors before trying more complex solving techniques in quadratic equations!

This page provides a step-by-step solution to the quadratic equation 2b^2 = 9b using the factoring method. Learn how to solve this algebraic problem by applying key concepts such as the Zero Product Property and factoring techniques. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation