Solve cos^2x + 2cosx + 1 = 0 for x over the interval [0, 2pi ). can someone give me a step by step answer. i don't understand at all.

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.

x=π  (in radians)  or    x=180º   (in degrees). 

It’s 11 because you add up all the sides 6+2+1+2 equals 11. Don’t forget your units!