To solve the quadratic equation 9x^2 + 3/4x - 2 = 0 by the method of completing the square, we should figure out what constant must be added and subtracted.
The process looks like this:
Firstly, we identify the coefficient of the x term, which is 'b', in our case it is 3/4.
The formula to calculate the term to add and subtract to complete the square is (b/2)^2.
So we take 3/4 and halve it to get 3/8
Next, we square this value. When (3/8)^2 = 0.140625 or 9/64.
So, to make it a perfect square, we must add and subtract 0.140625 or 9/64 from the equation 9x^2 + 3/4x - 2 = 0.
So, the answer is (D) 9/64.