Let's solve the equation \( x^2 + 3 = 0 \) step by step.
Step 1: Start with the original equation.
\[ x^2 + 3 = 0 \]
Step 2: Isolate the \( x^2 \) term.
\[ x^2 = -3 \]
Step 3: Take the square root of both sides.
\[ \sqrt{x^2} = \pm \sqrt{-3} \]
Step 4: Since \( \sqrt{-3} \) involves the imaginary unit \( i \), we can express it as follows:
\[ x = \pm i\sqrt{3} \]
Conclusion:
The solutions are complex and not real. Therefore, there are no real values of \( x \).
Solutions: There are no real solutions for this equation. The solutions are \( x = i\sqrt{3} \) and \( x = -i\sqrt{3} \).