10.1. Solve the equation $|x+1|=x^{2}+3 x+1$.
Answer: $x_{1}=0, x_{2}=-2-\sqrt{2}$. Solution. If $x \geq-1$, then we have $x^{2}+2 x=0 \Rightarrow x=0$ (the root $x=-2$ does not satisfy the condition $x \geq-1$ ). If $x<-1$, then we have $x^{2}+4 x+2=0 \Rightarrow x=-2-\sqrt{2}$ (the root $-2+\sqrt{2}$ does not satisfy the condition $x<-1$ ).