To complete the square we have to divided the linear coefficient by 2, and then squared it. In this case
[tex]\begin{gathered} y^2-5y+(-\frac{5}{2})^2 \\ =y^2-5y+\frac{25}{4} \end{gathered}[/tex]
to factor it we have to remember that this will always be the squared term plus what we add (before squaring). Then
[tex]\begin{gathered} y^2-5y+(-\frac{5}{2})^2=y^2-5y+\frac{25}{4} \\ =(y-\frac{5}{2})^2 \end{gathered}[/tex]
