Solve the Quadratic Inequality: -x² - 25 < 0

To solve the inequality $-x^2 - 25 < 0$, we start by simplifying it. Rearrange the inequality:

$-x^2 < 25$

Multiplying through by $-1$ (reversing the inequality sign), we have:

$x^2 > -25$

Since $x^2$ is always non-negative for all real numbers (i.e., $x^2 \geq 0$), the smallest value $x^2$ can take is $0$. Therefore, $x^2$ is always greater than $-25$, since any non-negative number is greater than a negative number. Thus, this inequality holds true for all real values of $x$.

Therefore, the solution to the inequality $-x^2 - 25 < 0$ is

All values of $x$.