Let's start by expanding the left side of the equation:

(x-7)(x+7) = x^2 + 7x - 7x - 49 = x^2 - 49

(x-1)^2 = (x-1)(x-1) = x^2 - x - x + 1 = x^2 - 2x + 1

Now, we can substitute these expanded expressions back into the original equation:

x^2 - 49 - (x^2 - 2x + 1) = 48

x^2 - 49 - x^2 + 2x - 1 = 48

-48 + 2x = 48

2x = 96

x = 48

So, the solution to the equation is x = 48.