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Benefactive

The benefactive is a noun case or an adposition which indicates movement towards or for someone. The preposition "for" is a benefactive preposition in English: "I did this for Bill".

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Quadratic formula

... form x2 + 2xy + y2. Since "2xy" in this case is (b/a)x, we must have y = b/(2a), so we add the square of b/(2a) to both sides, ...