2x^2 - 3x = -1
x^2 - (3/2)x = -1/2
There's a -3/2 on the x in the middle. Half of -3/2 is -3/4. -3/4 squared is 9/16.
x^2 - (3/2)x + 9/16 = -1/2 + 9/16
(x - 3/4)^2 = -1/2 + 9/16
(x - 3/4)^2 = -8/16 + 9/16
(x - 3/4)^2 = 1/16
x - 3/4 = +-sqrt(1/16)
x - 3/4 = +- 1/4
x = +- 1/4 + 3/4
x = 2/4 or 4/4
x = 1/2 or x = 1