Final answer:
To solve (x-6)^2=25, we find the positive and negative square roots of 25, leading to x = 11 and x = 1 as the final solutions.
Step-by-step explanation:
To solve the equation (x-6)^2=25, we recognize that this is a matter of finding the square roots of 25. Given the property that if a^2 = b, then a is equal to the positive and negative square roots of b, we can write two separate equations:
For the first equation, we add 6 to both sides to find x = 11. For the second equation, adding 6 to both sides gives us x = 1. Therefore, the two solutions to the equation are x = 11 and x = 1. Unlike more complex quadratic equations, which often require the quadratic formula or completing the square, this equation is straightforward due to the perfect square on the left-hand side.