Find the values of the integers x and y: 10x^(2)-90x+2xy+y^(2)+225=0

  (x, y) = (5, -5)

Step-by-step explanation:

The equation can be rewritten as ...

  9x^2 -90x +225 +x^2 +2xy +y^2 = 0

  9(x^2 -10x +25) +(x +y)^2 = 0

  9(x -5)^2 +(x +y)^2 = 0

The only way the sum of squares can be zero is for each square to be zero:

  x -5 = 0

  x +y = 0

Then x = 5 and y = -5.

-14 is the answer

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where is the figure