Answer
The trinomial that we get after completing the square is
$x^{2}-10x+25$.
This can be factored as
$x^{2}-10x+25=(x-5)^{2}$.
Work Step by Step
Comparing $x^{2}-10x$ with $x^{2}+bx$, we see that $b=-10$.
$(\frac{b}{2})^{2}=(\frac{-10}{2})^{2}=25$.
We can complete the square by adding $(\frac{b}{2})^{2}$ to $x^{2}+bx$. Then, the trinomial we get is
$x^{2}-10x+25$.
This can be factored as
$x^{2}-10x+25=(x-5)^{2}$
