Question

Find all solutions to the equation. cos^2x + 2 cos x + 1 = 0

Answer 1

$\cos^2(x)+2\cos(x)+1=0\\\\ (\cos(x)+1)^2=0\\\\ \text{So:}\\\\ \cos(x)+1=0\\\\ \cos(x)=-1\\\\ \boxed{x=\pi+2k\pi},~k\in\mathbb{Z}$

Answer 2

Hope this helps you.