Answer
We will add $\frac{25}{4}$ to make $x^2-5x$ a perfect square trinomial.
Work Step by Step
We add the square of half of the coefficent of $x$ so that the result is a perfect square trinomial.
Co-efficient of $x=-5$
Half of -5 is $\frac{1}{2}×-5=\frac{-5}{2}$
Square of $\frac{-5}{2}$ is $\frac{-5}{2}×\frac{-5}{2}=\frac{25}{4}$
We add $\frac{25}{4}$ to $x^2-5x$ to make it a perfect square trinomial.
