on in the image appears to be:

9
x
2
−
36
x
+
27
=
0
9x 
2
 −36x+27=0

The equation you have provided is:

\[
9x^2 - 36x + 27 = 0
\]

This is a quadratic equation, and we can solve it by factoring, completing the square, or using the quadratic formula. Here's how to solve it:

### Step 1: Simplify the Equation
First, we can simplify the equation by dividing every term by 9:

\[
x^2 - 4x + 3 = 0
\]

### Step 2: Factor the Quadratic Equation
Next, let's factor the quadratic expression:

\[
x^2 - 4x + 3 = (x - 3)(x - 1) = 0
\]

### Step 3: Solve for \( x \)
To find the solutions, set each factor equal to zero:

\[
x - 3 = 0 \quad \text{or} \quad x - 1 = 0
\]

So, the solutions are:

\[
x = 3 \quad \text{or} \quad x = 1
\]

### Final Answer
The solutions to the equation \( 9x^2 - 36x + 27 = 0 \) are:

\[
x = 3 \quad \text{and} \quad x = 1
\]

Would you like further details or have any questions? 

Here are 5 related questions for further exploration:

1. How can you verify the solutions to the quadratic equation by substitution?
2. What are the steps to solve a quadratic equation using the quadratic formula?
3. How would the solutions change if the quadratic equation had no real roots?
4. Can you solve the equation by completing the square, and how does it compare to factoring?
5. How does the discriminant determine the nature of the roots for a quadratic equation?

**Tip:** Always simplify the equation first, if possible, to make the solving process easier.

Learn how to solve the quadratic equation 9x^2 - 36x + 27 with a detailed step-by-step solution. This problem involves factoring quadratic expressions and solving equations. Suitable for students in Grades 9-12.

Math Problem Statement

9 x 2 − 36 x + 27

Solution

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