Chapter 11 - Quadratic Functions and Equations - 11.1 Quadratic Equations - 11.1 Exercise Set - Page 706: 25

$x=-1\pm 3i$

Since $x^2=a$ implies $x=\pm\sqrt{a}$ (the Square Root Principle), the solutions to the given equation, $ (x+1)^2=-9 ,$ are \begin{array}{l}\require{cancel} x+1=\pm\sqrt{-9} \\\\ x+1=\pm\sqrt{-1}\cdot\sqrt{9} \\\\ x+1=\pm i\cdot\sqrt{(3)^2} \\\\ x+1=\pm 3i \\\\ x=-1\pm 3i .\end{array}