To demonstrate that the solution to the quadratic equation x^2 - 4x = 4 is consistent across different methods, we can analyze each approach:

1. **Graphical Method**: By plotting the graph of y = x^2 - 4x and the line y = 4, we find the x-values where these two graphs intersect. This intersection represents the solutions to the equation.

2. **Factoring Method**: We rearrange the equation to x^2 - 4x - 4 = 0. This can be factored as (x - 2)(x - 2) = 0, leading to the solution x = 2.

3. **Quadratic Formula Method**: Using the quadratic formula x = (-b ± √(b² - 4ac)) / (2a), we identify a = 1, b = -4, and c = -4. Substituting these values gives us x = (4 ± √(16 + 16)) / 2, which simplifies to x = 2 ± 2√2. This indicates two solutions, but the primary solution we are interested in is x = 2.

In conclusion, all methods confirm that x = 2 is a solution to the quadratic equation, illustrating the consistency of mathematical approaches.