To transform the quadratic expression x² + 2x into a perfect square trinomial, we need to complete the square. A perfect square trinomial is of the form (a + b)², which expands to a² + 2ab + b².
Looking at x² + 2x, we can identify:
- a = x (since it is the coefficient of x²)
- 2ab = 2x (for our case, this means 2 * x * b = 2x for some value of b)
In this case, to find b, we can rearrange:
- 2b = 2
- b = 1
Next, we need to determine the value of b² to complete the square:
- b² = 1² = 1
Thus, to complete the square, we need to add 1 to the expression x² + 2x.
This gives us:
- x² + 2x + 1
Now, x² + 2x + 1 can be factored as (x + 1)², which is indeed a perfect square trinomial.
In conclusion, the number that should be added to the expression x² + 2x to change it into a perfect square trinomial is 1.