Solve the equation $\sqrt{1+\{2x\}}=\lfloor x^2\rfloor+2\lfloor x\rfloor+3$ (where $\{a\}=a-\lfloor a\rfloor$).
Source: Ukraine 1998 Grade 11 P1
Tags: floor function, algebra, equations, equation
Solve the equation $\sqrt{1+\{2x\}}=\lfloor x^2\rfloor+2\lfloor x\rfloor+3$ (where $\{a\}=a-\lfloor a\rfloor$).