To solve the quadratic equation (x^2 - 2x - 35 = 0), we can factor the quadratic or use the quadratic formula.

Factoring:
(x^2 - 2x - 35 = 0)
((x - 7)(x + 5) = 0)

Setting each factor to zero gives us the solutions:
(x - 7 = 0 \Rightarrow x = 7)
(x + 5 = 0 \Rightarrow x = -5)

So the solutions to the quadratic equation (x^2 - 2x - 35 = 0) are (x = 7) and (x = -5).