find the general solution of 2 cos x + 1 = 0

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First solve for cos x:  cos x = -1/2 You need to identify all radian values that have a cosine value of -1/2 You need to know that the cosine function is defined as the x coordinate of the ordered pairs associated with various radian measures on the unit circle. Specifically, the x coordinate is -1/2 at (2π)/3 and (4π)/3. Cosine is a periodic function with a period of 2π. Since you want the general solution you need to add multiples of  2π to each of the unit circle solutions. Final answer: x = (2π)/3 + 2πn and (4π)/3 + 2πn