the product of 2 consecutive odd integers is 27 plus 6 times the sum of the integers. what is the larger integer

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You can write two consecutive odd integers as x and x+2. The product of 2 consecutive integers, then is: x(x+2) The sum of the integers is: x+(x+2). So, you get, x(x+2) = 27+6(x+(x+2)) x^2+2x = 27+6(2x+2) x^2+2x = 27+12x+12 x^2-10x-39 = 0 and then go on to solve for x (your largest integer is going to be x+2). Note also (for factoring) that -13*3=-39, and -13+3=10.

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