amath trigo

16cos2x + 2sin2x + 42cos2x= 40
16cos2x + 2(1 - cos2x) + 16cos2x= 40
162 - cos2x + 16cos2x= 40
(16)2 (16) - cos2x + 16cos2x= 40
162 + [16(cos2x)]2= (40)(16)(cos2x)
[16(cos2x)]2 - (40)(16)(cos2x) + 162 = 0
[16(cos2x)]2 - (40)(16)(cos2x) + 256= 0
[16(cos2x)]2 - (40)(16)(cos2x) + (32)(8)= 0
(16cos2x - 8)(16cos2x - 32) = 0
16cos2x - 8 = 0　or　16cos2x - 32 = 0
24cos2x - 23 = 0　or　24cos2x - 25 = 0
24cos2x = 23　or　24cos2x = 25
4cos2x = 3　or　4cos2x = 5
cosx = (±√3)/2　or　cosx = (±√5)/2 (rejected as >1)
x = nπ ± π/6　( x = 180°n ± 30°)