Final answer:
The equation z - 5 = z - 25 does not have a solution as subtracting z from both sides leads to the false statement -5 = -25.
Step-by-step explanation:
The given equation to solve is z - 5 = z - 25. Completing the square is a method used to solve quadratic equations, but in this case, the equation is linear and simplifies easily.
Both sides of the equation contain the variable z, so when we subtract z from both sides, we can see there is no variable term left, and we end up with -5 = -25, which is not true.
This means that there is no solution to this equation because the two sides of the equation cannot equal each other for any value of z.