Question 1175397
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    x² + y² + 8x + 8y = 0


    (x^2 + 8x) + (y^2 + 8y) = 


    (x*2 + 8x + 16) + (y^2 + 8y + 16) = 16 + 16


Make a square


    {{{(x+4)^2}}} + {{{(y+4)^2}}} = 32


It is the standard equation of the circle centered at the point (-4,-4) with the radius of  {{{sqrt(32)}}} = {{{4*sqrt(2)}}} units.
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Solved.