Adding & subtracting i guess, Mathematics

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Jack and his mother paid $11.50 for tickets to the movies, and adults tickets cost $4.50 more than a child ticket what was the cost of each ticket?

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Solve : 4x2+2x+3=0 Ans) x^2 + (1/2)x = -(3/4) (x+1/4)^2 = 1/16 - 3/4 = -11/16 implies x = (-1+i(11)^(1/2))/4 and its conjugate.

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