I need help asap!!

Question

Find all of the answers on the interval [0,2π)

2cos2x+cosx=0

Give exact answers.

Answer 1

2cos2x+cosx=0

same as

2*(2*cos²x-1)+cos(x)=0

quadradic for cos(x)

correction (examined graph and saw little problem).

cos(x)=(-1/8)√±(√(1+32))8

cos(x)=-(1/8)+(√33)/8,,,x=53.6 degrees and 306.4 degrees

cos(x)=-(1/8)-(√33)/8,,,,,x=147.5 degrees and 212.5 degrees

Answer 2

Using double angle formula

2(2 cos² x - 1) + cos x = 0

Expand then use Zero-Factor Rule.