Answer:
see below
Step-by-step explanation:
x^2 - x + 3/16 = 0
Subtract 3/16 from each side
x^2 - x + 3/16 - 3/16 =  -3/16
x^2 -x = -3/16
Take the coefficient of x
-1 
Divide by 2
-1/2   call this a
Square it
(-1/2)^2 = 1/4
Add it to each side
x^2 - x +1/4 =- 3/16+1/4
Changing to the "square"
( x +a)^2 =  - 3/16+1/4 
getting a common denominator
( x -1/2) ^2 = -3/16+ 4/16
  ( x -1/2) ^2 =1/16
Take the square root of each side
sqrt(  ( x -1/2) ^2)  = ± sqrt(1/16)
x -1/2 = ± 1/4
Add 1/2 to each side
x -1/2 + 1/2 = 1/2 ± 1/4
x = 1/2 ± 1/4
Separate into 2 equations
x = 1/2 + 1/4                 x = 1/2 - 1/4
     2/4 +1/4                          2/4 -1/4
         3/4                                    1/4