[tex]x^2+6x+9=12\\\\x^2+2\cdot x\cdot3+3^2=12\\\\(x+3)^2=12\\\\(x+3)^2=\big(\sqrt{12}\big)^2\\\\(x+3)^2=\big(\sqrt{4\cdot3}\big)^2\\\\(x+3)^2=\big(\sqrt{4}\cdot\sqrt{3}\big)^2\\\\(x+3)^2=\big(2\sqrt{3}\big)^2\\\\(x+3)^2-\big(2\sqrt{3}\big)^2=0\\\\(x+3-2\sqrt{3})(x+3+2\sqrt{3})=0\\\\\\\boxed{x=-3+2\sqrt{3}\qquad\vee\qquad x=-3-2\sqrt{3}}[/tex]
