To solve this equation, we first need to isolate the cosine function by moving the constant terms to the other side of the equation.

Starting equation: cos*(x/2 + p/4) + 1 = 0

Subtract 1 from both sides: cos*(x/2 + p/4) = -1

Now we need to find where the cosine function equals -1. The cosine function equals -1 when the angle inside the cosine function is (2n+1)π, where n is an integer.

So we set the argument of the cosine function equal to (2n+1)π:

x/2 + p/4 = (2n+1)π

Solve for x:

x/2 = (2n+1)π - p/4
x = 2((2n+1)π - p/4)

Thus, the solution to the equation cos*(x/2 + p/4) + 1 = 0 is x = 2((2n+1)π - p/4), where n is an integer.