To transform the expression x² + 2x into a perfect square trinomial, we need to complete the square.
The general form of a perfect square trinomial is (x + a)², which expands to x² + 2ax + a². Here, the coefficient of x (which is 2 in our case) can be related to 2a, where a is half of that coefficient.
In our expression, the coefficient of x is 2. Dividing that by 2 gives us:
- a = 2 / 2 = 1
Next, we square this value of a:
- a² = 1² = 1
Therefore, to convert x² + 2x into a perfect square trinomial, we need to add 1. This will give us:
- x² + 2x + 1 = (x + 1)²
So, the number that should be added is 1.