We want to make x^2-3x into a perfect square trinomial. An example of such a trinomial is x^2 + 6x + 9, which is equivalent to the square of (x+3).
From x^2-3x we see that the coefficient of x is -3. Divide this coefficient, -3, by 2, obtaining -3/2. Now square this result: square -3/2. Result: 9/4.
Adding 9/4 to x^2-3x makes x^2-3x into a perfect square trinomial.
