To rewrite the equation in the indicated form, isolate the variable terms on the left side of the equation.
[tex]8x^2+9y^2-16x-9y=-2[/tex]
Group the variable terms and then complete the squares. Add the same terms on the right side of the equation to make it balance.
[tex]\begin{gathered} (8x^2-16x)+(9y^2-9y)=-2 \\ 8(x^2-2x)+9(y^2-y)=-2 \\ 8(x^2-2x+1)+9(y^2-y+\frac{1}{4})=-2+8+9(\frac{1}{4}) \end{gathered}[/tex]
Rewrite the trinomials as squares of binomials and then simplify the right side of the equation.
[tex]8(x-1)^2+9(y-\frac{1}{2})=\frac{33}{4}[/tex]
To make the right side of the equation equal to 1, multiply both sides of the equation by 4/33.
[tex]\begin{gathered} \mleft(\frac{4}{33}\mright)(8)(x-1)^2+\mleft(\frac{4}{33}\mright)(9)(y-\frac{1}{2})=\mleft(\frac{4}{33}\mright)\mleft(\frac{33}{4}\mright) \\ \frac{32\mleft(x-1\mright)^2}{33}+\frac{12(y-\frac{1}{2})}{11}=1 \end{gathered}[/tex]
