To make the expression x² + 10x a perfect square trinomial, we need to find a value that can be added to complete the square.
A perfect square trinomial takes the form (x + a)², which expands to x² + 2ax + a². In our case, we have:
- Here, the coefficient of x is 10, which can be expressed as 2a. This means that:
2a = 10
- This leads to:
a = 5
- To complete the square, we must add a²:
a² = 5² = 25
Thus, to make x² + 10x a perfect square trinomial, we need to add 25. The complete expression becomes:
x² + 10x + 25 = (x + 5)²
So, the correct value to add is 25.