We need to expand the answer choices and see which one matches the equation
[tex]x^2+4x+15=0[/tex]Remember the algebraic rules:
[tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]Now, if we expand choice D, we should get this. Let's expand:
[tex]\begin{gathered} (x+2)^2=-11 \\ x^2+2(1)(2)+(2)^2=-11 \\ x^2+4x+4=-11 \\ x^2+4x+4+11=0 \\ x^2+4x+15=0 \end{gathered}[/tex]