1. Problem: Solve the inequality $x^2 + 3 > 0$. 2. Formula and rules: For any real number $x$, $x^2 \geq 0$. Adding 3 makes it strictly positive. 3. Intermediate work: Since $x^2 \geq 0$, then $x^2 + 3 > 0$ for all real $x$. 4. Explanation: The square of any real number is non-negative, so adding 3 ensures the expression is always greater than zero. 5. Final answer: $\boxed{\text{All real numbers } x \in (-\infty, \infty)}$.