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X^2 - 6X + 12 = 0

X^2 - 6X = -12

halve the linear term (-6), square it and add it to both sides

X^2 - 6X + 9 = -12 + 9

gather terms right side, factor terms left side

(X - 3)^2 = -3

(X - 3)^2 + 3 = 0

(3,3) are the vector coordinates

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