Sin(π/4*(x-7)) = -√2/2

First, we need to find the angle whose sine is -√2/2. This angle is -π/4.

So, we have:

π/4*(x-7) = -π/4 + 2nπ, where n is an integer

Now, we solve for x:

x-7 = -1 + 8n

x = 6 + 8n

So, the solutions to the equation are x = 6, 14, 22, ...