Final answer:
To complete the perfect square trinomial x²+3x, we need to find the value that, when added to the expression, will result in a perfect square trinomial.
Step-by-step explanation:
To determine the value that would complete the perfect square trinomial x²+3x, we need to find the missing term that, when added to the expression, will result in a perfect square trinomial.
A perfect square trinomial can be written as (x + k)², where k is a constant.
In this case, we need to find the value of k. We can do this by taking half of the coefficient of x and squaring it. In this expression, the coefficient of x is 3, so half of 3 is 1.5, and squaring 1.5 gives us 2.25.
Therefore, the value that would complete the perfect square trinomial x²+3x is 2.25.