Решите уравнение √2 + 2cos (5x + п/3) = 0

Решите задачу:

$\sqrt{2}+2cos(5x+ \frac{\pi}{3} )=0 \\2cos(5x+ \frac{\pi}{3} )=-\sqrt{2} \\cos(5x+ \frac{\pi}{3} )=- \frac{\sqrt{2}}{2} \\5x+ \frac{\pi}{3} = \frac{3\pi}{4} +2\pi n \\5x= \frac{3\pi}{4}-\frac{\pi}{3} +2\pi n \\5x= \frac{5\pi}{12} +2\pi n \\x_1= \frac{\pi}{12} + \frac{2\pi n}{5} ,\ n \in Z \\5x+ \frac{\pi}{3} = -\frac{3\pi}{4} +2\pi n \\5x=-\frac{3\pi}{4} -\frac{\pi}{3} +2\pi n \\5x=- \frac{13\pi}{12} +2\pi n \\x_2=- \frac{13\pi}{60} + \frac{2\pi n}{5} ,\ n \in Z$