SOLUTION: Find the sum of four consecutive negative integers, such that the square of the sum of the first and fourth is 289.

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Question 912400: Find the sum of four consecutive negative integers, such that the square of the sum of the first and fourth is 289.
Answer by CubeyThePenguin(3113) About Me  (Show Source):
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consecutive integers: x, (x+1), (x+2), (x+3)


(x + (x+3))^2 = 289
(2x+3)^2 = 289
4x^2 + 12x + 9 = 289
4x^2 + 12x - 280 = 0
x^2 + 3x - 70 = 0
(x + 10)(x - 7) = 0

The integers are negative, so x = -10 and the integers are -10, -9, -8, and -7.