The given quadratic equation is:

$4x^2 - 12x + 9 = 0$

This equation can be solved by factoring or using the quadratic formula. Let's attempt factoring first.

Factoring the quadratic expression:

The equation can be rewritten as:

$(2x - 3)^2 = 0$

To solve for $x$, we take the square root of both sides:

$2x - 3 = 0$

Solving for $x$:

$x = \frac{3}{2}$

Conclusion:

The solution to the equation $4x^2 - 12x + 9 = 0$ is:

$x = \frac{3}{2}$

It is a repeated root (also known as a double root), meaning the quadratic has only one unique solution.

Would you like further details or have any questions?

Related questions:

1. What is a double root, and why does it occur?
2. How does completing the square solve quadratics?
3. Can every quadratic equation be factored like this?
4. How is the discriminant used to determine the number of roots?
5. What are the steps for solving quadratic equations using the quadratic formula?

Tip:

If a quadratic equation can be factored into a perfect square, it will have a repeated root.