$$\eqalign{
& \cos 2x + 5\cos x + 1 = 0 \cr
& \Leftrightarrow 2{\cos ^2}x - 1 + 5\cos x + 1 = 0 \cr
& \Leftrightarrow 2{\cos ^2}x + 5\cos x = 0 \cr
& \Leftrightarrow \cos x\left( {2\cos x + 5} \right) = 0 \cr
& \Leftrightarrow \left[ \matrix{
\cos x = 0 \hfill \cr
2\cos x + 5 = 0 \hfill \cr} \right. \cr
& \Leftrightarrow \left[ \matrix{
\cos x = 0 \hfill \cr
\cos x = - {5 \over 2}\,\,\left( {loai} \right) \hfill \cr} \right. \cr
& \Leftrightarrow x = {\pi \over 2} + k\pi \,\,\,\left( {k \in Z} \right) \cr} $$
