To transform the expression x² + 10x into a perfect square trinomial, we need to find a constant that will complete the square. A perfect square trinomial can be expressed in the form (a + b)², which expands to a² + 2ab + b².
In our case, we have:
x² + 10x = (x + 5)² – 25
Here, we identify that:
- a = x
- b = 5
To complete the square, we calculate b²:
b² = 5² = 25
Thus, to convert x² + 10x into a perfect square trinomial, we need to add 25.
In conclusion, the constant that can be added to x² + 10x to make it a perfect square trinomial is 25. Therefore, adding 25 gives us:
x² + 10x + 25 = (x + 5)².