Final answer:
To make x²+x a perfect-square trinomial, we need to add 1/4.
Step-by-step explanation:
An expression is a perfect-square trinomial if it can be factored into the square of a binomial. To make the expression x²+x a perfect-square trinomial, we need to find the value that can be added to it. In this case, we can complete the square by adding the square of half the coefficient of x, which is 1/2.
Let's add (1/2)² = 1/4 to the expression:
x² + x + 1/4
Now, we can factor this expression into a perfect-square trinomial:
(x + 1/2)²
Therefore, the value that must be added to the expression x²+x to make it a perfect-square trinomial is 1/4.
Learn more about Perfect-square trinomial