We are given the quadratic equation:

\[
4x^2 - 12x + 9 = 0
\]

### Step 1: Recognize that this is a perfect square

Notice that this equation can be factored as a perfect square. Let's rewrite it:

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

You can check this by expanding \( (2x - 3)^2 \):

\[
(2x - 3)(2x - 3) = 4x^2 - 6x - 6x + 9 = 4x^2 - 12x + 9
\]

This shows that the equation is a perfect square.

### Step 2: Solve the equation

Since \( (2x - 3)^2 = 0 \), we can take the square root of both sides:

\[
2x - 3 = 0
\]

### Step 3: Solve for \(x\)

Add 3 to both sides:

\[
2x = 3
\]

Now, divide both sides by 2:

\[
x = \frac{3}{2}
\]

### Final Answer:
The solution to the equation is:

\[
x = \frac{3}{2}
\]

### Recap:
1. Recognize the quadratic as a perfect square.
2. Factor the quadratic expression.
3. Solve by setting the factor equal to zero and solving for \(x\).

Would you like more details or additional practice?

Here are 5 related questions for further practice:

1. How do you solve \( x^2 - 6x + 9 = 0 \)?
2. Can you factor and solve \( 9x^2 - 12x + 4 = 0 \)?
3. How do you solve a quadratic equation like \( x^2 + 4x - 12 = 0 \)?
4. What happens when the quadratic does not factor easily, like \( 2x^2 - 3x + 5 = 0 \)?
5. How do you solve quadratic equations using the quadratic formula?

**Tip:** Always check if a quadratic equation can be factored as a perfect square. This can save time and simplify the solving process.

Learn how to solve the quadratic equation 4x^2 - 12x + 9 = 0 with a detailed, step-by-step solution. This problem involves factoring a perfect square and solving for x. Suitable for students in Grades 8-10.

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