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If: y = x-1 then y^2 = (x-1)^2

If: x^2 +y^2 = 1 then x^2 +(x-1)^2 -1 = 0

Multiplying out brackets: x^2 +x^2 -2x +1 -1 = 0

Collecting like terms: 2x^2 -2x = 0

Dividing all terms by 2: x^2 -x = 0

Completing the square: (x-0.5)^2 = 0.25

Square root both sides: x-0.5 = -0.5 or +0.5

Add 0.5 to both sides: x = 0 or x = 1

Points of contact by substitution x into original equations are at (0, -1) and (1, 0)

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