To make the expression x² + x a perfect square trinomial, we need to add a specific value that will allow the expression to form a square of a binomial.
A perfect square trinomial can be expressed in the form (a + b)², which expands to a² + 2ab + b². In our expression, x² + x, we have a² as x² and 2ab corresponding to the linear term x.
To find b, we can equate it to half the coefficient of x in our expression, which is 1. Therefore, b = 1/2. Now, we can calculate b²: (1/2)² = 1/4.
This means we need to add 1/4 to the expression to make it a perfect square trinomial. So, the resulting expression becomes:
x² + x + 1/4 = (x + 1/2)².
Thus, the value that must be added to the expression x² + x to make it a perfect square trinomial is 1/4.