Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - Exercise Set - Page 593: 41

{$-1-i,-1+i$}

Given: $x^2+2x+2=0$ This can be re-written as: $x^2+2x=-2$ We need to add $(1)^2$ to complete the square. Thus, $x^2+2x+1=-2+1$ or, $(x+1)^2=-1$ or, $(x+1)=\pm \sqrt {-1}$ or, $x=-1+i,-1-i$ Hence, solution set is $x=${$-1-i,-1+i$}