Question 760858
{{{36x^2-y^2-24x+6y-91=0}}}


{{{36x^2-24x-y^2+6y=91}}}
{{{(36x^2-24x)-(y^2-6y)=91}}}
Now DIVIDE the x expression by 36 and indicate a factor of 36 applied to the x expression.
{{{36(x^2-(24/36)x)-(y^2-6y)=91}}}
{{{36(x^2-(2/3)x)-(y^2-6y)=91}}}


The missing square term for the x part is {{{(2/(2*3))^2=1/9}}}
and
The missing square term for the y part is {{{(6/2)^3=9}}}


Watch the signs and factors very carefully when you ADD the square terms to both sides of the equation, because this can be the source of mistakes.