cos²x+2cos x+1=0
We have to do a change of variable.
cos x=t
Then, we have the next square equation.
t²+2t+1=0
We solve this square equation:
t=[-2⁺₋√(4-4)]/2=-1
if cos x=t then we have that:
cos x=-1
x=cos⁻¹ -1= π radians or 180º.
Answer: x=π (in radians) or x=180º (in degrees).