Given the expression:
[tex](x+4)²=-7[/tex]if we apply the square root on both sides of the equation, we get the following:
[tex]\begin{gathered} \sqrt{(x+4)²}=\pm\sqrt{-7} \\ \Rightarrow x+4=\pm\sqrt{7}i \end{gathered}[/tex]solving for x, we get:
[tex]\begin{gathered} x+4=\pm\sqrt{7}i \\ \Rightarrow x=-4\pm\sqrt{7}i \end{gathered}[/tex]therefore, the solutions are -4+sqrt(7)i and -4-sqrt(7)i
