Solve x² + 4 > 0: Understanding Quadratic Inequalities

To solve this problem, let's examine the inequality $x^2 + 4 > 0$.

The expression $x^2 + 4$ consists of two terms: $x^2$ and $4$. Notice that:

• The term $x^2$ is always non-negative, which means $x^2 \geq 0$ for any real number $x$.
• The constant term $4$ is positive.

Combining these observations, we see that:

• Since $x^2$ is non-negative, $x^2 + 4 \geq 4$.
• Therefore, $x^2 + 4$ is always greater than zero, as adding 4 to a non-negative number will always yield a positive result.

Thus, there are no values of $x$ for which the expression $x^2 + 4$ is zero or negative. Instead, the expression is always positive for all real numbers $x$.

Therefore, the solution to the inequality $x^2 + 4 > 0$ is all values of $x$.