To solve the quadratic equation \( 3x^2 + 5 - 2 = 0 \), we first simplify it:

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

Now, subtract 3 from both sides:

\[
3x^2 = -3
\]

Next, divide both sides by 3:

\[
x^2 = -1
\]

Since \( x^2 = -1 \), take the square root of both sides:

\[
x = \pm \sqrt{-1}
\]

Since \( \sqrt{-1} = i \) (where \( i \) is the imaginary unit), the solution is:

\[
x = \pm i
\]

### Final Solution:
\[
x = i \quad \text{or} \quad x = -i
\]

Do you want more details on complex numbers or have any questions?

### 5 Related Questions:
1. How do we solve quadratic equations with real solutions?
2. What are imaginary numbers and how are they used in mathematics?
3. How can we use the quadratic formula for solving more complex equations?
4. What is the significance of complex numbers in real-world applications?
5. How can we graph complex numbers on the complex plane?

### Tip:
When encountering a negative number under a square root, the solution involves complex numbers using the imaginary unit \( i \), where \( i^2 = -1 \).

Explore how to solve the quadratic equation 3x² + 3 = 0, where the solutions involve complex numbers. This detailed guide covers the use of imaginary numbers and the square root property, ideal for students in Grades 10-12.

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