The equation $x^2 + 2 = 0$ can be solved as follows:

1. Start with the equation: $x^2 + 2 = 0$

2. Subtract 2 from both sides: $x^2 = -2$

3. Take the square root of both sides: $x = \pm \sqrt{-2}$

4. Simplify using imaginary numbers (since the square root of a negative number involves $i$, where $i^2 = -1$): $x = \pm \sqrt{2}i$

Final Answer:

$x = \pm \sqrt{2}i$

Would you like a detailed explanation on imaginary numbers or any other related concepts?

Related Questions:

1. What are imaginary numbers and how are they used in mathematics?
2. Can this equation have any real solutions?
3. How does the square root of negative numbers work?
4. What is the significance of the imaginary unit $i$?
5. Are there real-world applications of imaginary numbers?

Tip:

When solving equations involving square roots of negative numbers, always check if imaginary numbers are part of the solution set you're working with!