Inspired by 'Floor Ceiling Ceiling Floor : JEE Style'

Algebra Level 4

$\large \displaystyle (\lceil x + 1 \rceil)^2 + (\lfloor x -1 \rfloor)^2 = (\lceil x -1 \rceil)^2 + (\lfloor x + 1 \rfloor)^2$

The solution set of the equation above is?

Notations:

$\mathbb{R}$ denote the set of real numbers.

$\mathbb{Z}$ denote the set of integers.

$\mathbb{N}$ denote the set of natural numbers.

$\mathbb{Q}$ denote the set of rational numbers.