Let's solve the equation:

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

Step 1: Simplify the constants on the left-hand side.

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

Step 2: Move the constant to the other side of the equation.

\[
4x^2 = 3
\]

Step 3: Divide both sides by 4 to isolate \(x^2\).

\[
x^2 = \frac{3}{4}
\]

Step 4: Take the square root of both sides.

\[
x = \pm \sqrt{\frac{3}{4}} = \pm \frac{\sqrt{3}}{2}
\]

So, the solutions are:

\[
x = \frac{\sqrt{3}}{2} \quad \text{or} \quad x = -\frac{\sqrt{3}}{2}
\]

Do you want further details on any part of this solution?

Here are 5 related questions:
1. How do you solve quadratic equations with complex solutions?
2. How do you simplify square roots of fractions?
3. What are the steps for completing the square in quadratic equations?
4. How do you factor quadratic equations instead of using the square root?
5. How does the quadratic formula apply to this kind of equation?

**Tip:** Always check if the quadratic equation can be factored before jumping into the square root or formula methods.

Learn how to solve the quadratic equation 4x^2 - 12 + 9 = 0 step by step using the square root method. This solution simplifies the equation and shows how to find both positive and negative roots. Ideal for students in Grades 9-10 studying algebra and quadratic equations.

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