Solve the inequation: $\;$ $2 - x - x^2 \geq 0$
Given inequation: $\;$ $2 - x - x^2 \geq 0$
i.e. $\;$ $x^2 + x - 2 \leq 0$
i.e. $\;$ $\left(x - 1\right) \left(x + 2\right) \leq 0$
i.e. $\;$ $x - 1 \leq 0 \; \cap \; x + 2 \geq 0$ $\;$ OR $\;$ $x - 1 \geq 0 \; \cap \; x + 2 \leq 0$
i.e. $\;$ $x \leq 1 \; \cap \; x \geq -2$ $\implies$ $x \in \left[-2, 1\right]$
OR $\;$ $x \geq 1 \; \cap \; x \leq -2$ $\;\;\;$ which is not possible
$\therefore \;$ The solution is $\;$ $x \in \left[-2, 1\right]$