to do a perfect-square trinomial the third term must be the square of the half of the second term
the sencond term is 7,so
[tex](\frac{7}{2})^2=\frac{49}{4}[/tex]so the expresion is
[tex]w^2+7w+\frac{49}{4}[/tex]and the factor
[tex](w+\frac{7}{2})^2[/tex]An example
[tex]w^2+\frac{8}{5}w+\cdots_{}[/tex]the third term is
[tex]\begin{gathered} (\frac{\frac{8}{5}}{2})^2 \\ \\ (\frac{4}{5})^2 \\ \\ =\frac{16}{25} \end{gathered}[/tex]so the percet-square is
[tex]w^2+\frac{8}{5}w+\frac{16}{25}[/tex]