The given quadratic expression is,
[tex]\begin{gathered} x^2+9x+35 \\ =\lbrace x^2+2(x)\times\frac{9}{2}+(\frac{9}{2})^2\rbrace-(\frac{9}{2})^2+35 \\ =\lbrace x^2+2(x)\times\frac{9}{2}+(\frac{9}{2})^2\rbrace-\frac{81}{4}^{}+35 \\ =\lbrace x^2+2(x)\times\frac{9}{2}+(\frac{9}{2})^2\rbrace-\frac{81}{4}^{}+35 \\ =\lbrace x^2+2(x)\times\frac{9}{2}+(\frac{9}{2})^2\rbrace+\frac{-81+140}{4}^{} \\ =\lbrace x^2+2(x)\times\frac{9}{2}+(\frac{9}{2})^2\rbrace+\frac{59}{4}^{} \end{gathered}[/tex]Thus, 81/4 must be added to complete
