[tex](*)\qquad(a+b)^2=a^2+2ab+b^2\\\\x^2+12x=-11\\\\x^2+2(x)(6)=-11\qquad\text{add}\ 6^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(6)+6^2}_{(*)}=-11+6^2\\\\(x+6)^2=-11+36\\\\(x+6)^2=25\to x+6=\pm\sqrt{25}\\\\x+6=-5\ \vee\ x+6=5\qquad\text{subtract 6 from both sides}\\\\\boxed{x=-11\ \vee\ x=-1}[/tex]
