2cosx -3 = -5 add 3 to both sides

2cosx = -5 +3 = -2

divide by 2

cosx =-2/2 =- 1

cosx =-1

x = pi radians or 180 degrees

x = cos^-1(-1)

one way to find x is use a calculator with an inverse trig function. Punch in -1 then punch the inverse cosine key

or sketch a unit circle and realize that cosine = adjacent side over hypotenuse = -1

cosines are negative only in the 2nd and 3rd quadrants. -1 is the minimum possible value of cosine of any angle. that's the boundary of quadrant 2 and 3, where x=pi or 180

Or draw the cosine curve, It equals 1 when x = 0, and reaches a minimum -1 when x= 180 or pi, half the period of 2pi