x^2 - (3/4)x + 1/8 = 0
There's a -3/4 on the x in the middle. Half of -3/4 is -3/8. -3/8 squared is 9/64.
x^2 - (3/4)x + 9/64 - 9/64 + 1/8 = 0
(x - 3/8)^2 - 9/64 + 1/8 = 0
(x - 3/8)^2 - 9/64 + 8/64 = 0
(x - 3/8)^2 - 1/64 = 0
(x - 3/8)^2 = 1/64
x - 3/8 = +- sqrt(1/64)
x - 3/8 = +- 1/8
x = +- 1/8 + 3/8
x = 2/8 or 4/8
x = 1/4 or x = 1/2