To solve the equation x - √(2x^2 - 3x) + 1 = 1, we can start by simplifying the equation:

x - √(2x^2 - 3x) + 1 = 1

Since 1 = 1, we can subtract 1 from both sides of the equation:

x - √(2x^2 - 3x) = 0

Next, let's isolate the square root term by moving x to the other side:

√(2x^2 - 3x) = x

Now, square both sides of the equation to eliminate the square root:

(√(2x^2 - 3x))^2 = x^2

2x^2 - 3x = x^2

Rearrange the equation to bring all terms to one side:

2x^2 - 3x - x^2 = 0

Combine like terms:

x^2 - 3x = 0

Factor out an x:

x(x - 3) = 0

Now, we have two possible solutions:

1) x = 0
2) x - 3 = 0
x = 3

Therefore, the solutions to the equation x - √(2x^2 - 3x) + 1 = 1 are x = 0 and x = 3.