What value must be added to the expression x2-3x to make it a perfect square trinomial

Answer: 9/4

Explanation:

1) Given: x^2 - 3x

2) A perfect square trinomial is the result of a binomial squared, for example:

(x + a) ^2 = x^2 + 2xa + a^2

So, since you have x^2 and - 3x, you have to add (3/2) ^2.

In that way you obtain x^2 - 3x + 9/4, which is (x - 3/2) ^2.

Prove it:

(x - 3/2) ^2 = x^2 - 2 * x * (3/2) + (3/2) ^2 = x^2 - 3x + 9/4. Meaning that x^2 - 3x + 9/4 is a perfect square trinomial.

So, you must add 9/4 to x^2 - 3x to make it a perfect square trinomial.