To solve the equation, we can take the square root of both sides:

√((x-1)^2) = √1

Simplifying, we have:

|x-1| = 1

This equation represents two separate equations:

x - 1 = 1 or x - 1 = -1

Solving each equation separately, we get:

For x - 1 = 1:
x = 1 + 1
x = 2

For x - 1 = -1:
x = -1 + 1
x = 0

Therefore, the solutions to the equation (x-1)^2 = 1 are x = 2 and x = 0.