To determine which constant can be added to the expression x² + 10x to form a perfect square trinomial, we follow a straightforward process.
A perfect square trinomial is typically in the form of (a + b)² or (a – b)², which expands to a² + 2ab + b². In our case, we need to analyze the existing quadratic expression x² + 10x.
1. **Identify the Coefficient of x**: In our expression, the coefficient of x is 10.
2. **Calculate b**: To find the necessary constant that needs to be added, we calculate b where b = 10 / 2. This gives us b = 5.
3. **Determine b²**: Next, we square this value to find the constant to add: b² = 5² = 25.
So, if we add the constant 25 to our expression, we have:
x² + 10x + 25
This expression is indeed a perfect square trinomial, as it can be factored into:
(x + 5)².
Therefore, the constant that should be added to x² + 10x to form a perfect square trinomial is 25.