Given
[tex]x^2+2x+y^2-6y=35[/tex]Complete the square for x, as shown below
[tex]\begin{gathered} x^2+2x+b=(x+a)(x+a)=x^2+2ax+a^2 \\ \Rightarrow2=2a\Rightarrow a=1 \\ \Rightarrow b=a^2=1 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} x^2+2x+1+y^2-6y=35+1=36 \\ \Rightarrow(x+1)^2+y^2-6y=36 \end{gathered}[/tex]Completing the square for y,
[tex]\begin{gathered} y^2-6y+b=(x+a)^2=x^2+2ax+a^2 \\ \Rightarrow-6=2a\Rightarrow a=-3 \\ \Rightarrow b=a^2=9 \end{gathered}[/tex]Then,
[tex](x+1)^2+(y-3)^2=45[/tex]