2. Solve the equation: $[x]\{x\}+x=2\{x\}+10$.
(1991, Recommended by the Soviet Ministry of Education for Competition Problems)
(Given that the equation can be factored as $([x]-1)(\{x\}+1)$ $=9$. Since $[x]-1$ is an integer, we know that $\{x\}+1$ is a rational number, and we can set $\{x\}$ $=\frac{n}{k}, 0 \leqslant n<k$. Then simplify the equation. $x=10,7 \frac{1}{2}, 9 \frac{1}{8}$, $\left.8 \frac{2}{7}, 6 \frac{4}{5}.\right)$