Solution
We want to complete the square of
[tex](x^2+8x)+(y^2-6y)=11[/tex]
Firstly, let us look at how to complete a square.
Consider the illustration below
[tex]\begin{gathered} To\text{ complete the square of }(x^2+8x) \\ Add\text{ \lparen}\frac{8}{2})^2\text{ to both sides of the equation} \\ That\text{ is 4}^2=16 \end{gathered}[/tex][tex]\begin{gathered} To\text{ complete the sqaure of y}^2-6y,\text{ } \\ Add\text{ \lparen}\frac{-6}{2})^2=(-3)^2=9\text{ to both sides of the equation} \end{gathered}[/tex]
Thus, we have
[tex](x^2+8x+16)+(y^2-6y+9)=11+_16+9[/tex][tex]\begin{gathered} The\text{ answer is } \\ (x^2+8x+16)+(y^2-6y+9)=11+16+9 \end{gathered}[/tex]
