No.
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x2 + 2y - 6x + 8y - 1 = x2 - y2 + 4x + 6y - 1 y2 - 10x + 4y = 0 y(y+4) = 10x It cannot be solved completely because with two variables (x and y) you need two independent equations for a full solution.
x2 + 2y = 52 + 2*2 = 25 + 4 = 29
Implicit: x2 + 2y = 5 Explicit : y = (5 - x2)/2
x2+4x+4 = 25 x2+4x+4-25 = 0 x2+4x-21 = 0 (x+7)(x-3) = 0 x = -7 or x = 3
x^2+4x+7