parmenides51 wrote: Solve the following equation where $x$ is a real number: $\lfloor x^2 \rfloor -10\lfloor x \rfloor + 24 = 0$ $$a^2 -10a + 24 = 0$$$$(a-6)(a-4) = 0$$$$a=4, 6$$$$\lfloor x \rfloor=4, 6$$$$4\le x< 5, 6\le x< 7$$