complete the square
4x^2 - 4x - 35 = 0
4(x^2 - x) - 35= 0
4(x^2 - x + 1/4 - 1/4) - 35 = 0
4(x^2 - x + 1/4) - 1 - 35 = 0
4(x^2 - x + 1/4) - 36 = 0
treat the equation as a difference of two squares,
4(x - 1/2)^2 - 6^2 = 0
factor
(2(x - 1/2) - 6) (2(x - 1/2)+ 6) = 0
(2x - 1 - 6)(2x - 1 + 6) = 0
simplify to the usual two factors.
(2x - 7)(2x + 5) = 0
