Find all values of x in the interval [0, 2𝜋] that satisfy the equation. (Enter your answers as a comma-separated list.)

Question

14 + 7 cos(2x) = 21 cos(x)

Answer 1

14 + cos 2x = 21 cos x

cos 2x = 21 cos x - 14

2 cos² x - 1 = 21 cos x - 14

Set equal to zero and solve using Zereo Product Rule (Algebra 2)

Answer 2

14+7cos2x =21cosx

2+cos2x =3cosx

2+2cos^2(x)-1=3cosx

let y=cosx

2y^2-3y+1=0

(2y-1)(y-1)=0

y=1/2=cosx, x=arccos.5 +360n n=any integer

= 60 +360n, -60+360n and

y=1=cosx, x=arccos1=0+360n= 360n

Answer 3