Chapter 8 - Section 8.1 - The Square Root Property and Completing the Square - Exercise Set - Page 593: 37

{$-3-\sqrt {7},-3+\sqrt {7}$}

Given: $x^2+6x=-2$ We need to add $3^2$ to complete the square. Thus, $x^2+6x+3^2=-2+9$ or, $x^2+(2)(1)(3x)+3^2=7$ or, $(x+3)^2=7$ or, $(x+3)=\pm \sqrt {7}$ or, $x=-3- \sqrt {7},-3+\sqrt {7}$ Hence, solution set is $x=${$-3-\sqrt {7},-3+\sqrt {7}$}