[tex](*)\qquad(a+b)^2=a^2+2ab+b^2\\\\x^2+4x=15\\\\x^2+2(x)(2)=15\qquad\text{add}\ 2^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(2)+2^2}_{(*)}=15+2^2\\\\(x+2)^2=15+4\\\\(x+2)^2=19\to x+2=\pm\sqrt{19}\qquad\text{subtract 2 from both sides}\\\\\boxed{x=-2-\sqrt{19}\ \vee\ x=-2+\sqrt{19}}[/tex]
