Let's solve the quadratic equation:

\[
36x^2 - 72x = 0
\]

### Step 1: Factor the equation
First, factor out the greatest common factor, which is 36x:

\[
36x(x - 2) = 0
\]

### Step 2: Set each factor to zero
For the product to be zero, either factor must be zero:

1. \( 36x = 0 \)  
   Dividing both sides by 36:
   \[
   x = 0
   \]

2. \( x - 2 = 0 \)  
   Adding 2 to both sides:
   \[
   x = 2
   \]

### Step 3: Solutions
The solutions to the equation are:

\[
\boxed{x = 0 \text{ and } x = 2}
\]

Would you like more details or have any questions?

Here are some related questions:
1. How do you solve quadratic equations using the quadratic formula?
2. What is factoring, and why is it useful in solving equations?
3. How do you find the roots of a polynomial?
4. Can all quadratic equations be solved by factoring?
5. What are the differences between solving linear and quadratic equations?

**Tip:** Always check if an equation can be factored before using more complex methods like the quadratic formula. It can save time!

This detailed step-by-step guide explains how to solve the quadratic equation 36x^2 - 72x = 0 using factoring. Learn key algebra concepts like the zero product property and factoring, 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