1. If the equation $\frac{-x}{\sqrt{x^{2}+2 x+2}}=a$ has real solutions, then the range of real number $a$ is
1. $(-1, \sqrt{2}]$ Detailed explanation: Let $f(x)=\frac{-x}{\sqrt{x^{2}+2 x+2}}, g(x)=a$. Since the range of the function $f(x)$ is $(-1, \sqrt{2}]$, we respectively draw the graphs of the functions $f(x)$ and $g(x)$. To ensure that the graphs of the two functions intersect, $a \in(-1, \sqrt{2}]$.