Question 1207930
{{{2x^2+8x+2y^2=-7}}}


{{{x^2+4x+y^2=-7/2}}}


the x-parts need some work.  The y-parts are fine.
Completing The Square requires 4.


{{{x^2+4x+y^2+4=-7/2+4}}}


{{{x^2+4x+4+y^2=-7/2+8/2}}}


{{{(x^2+4x+4)+y^2=1/2}}}------------You take it from here!