# SOLUTION: How do I solve this verbal problem with a quadratic equation? The sum of the squares of two consecutive negative integers is forty-one.

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 Question 412046: How do I solve this verbal problem with a quadratic equation? The sum of the squares of two consecutive negative integers is forty-one.Found 2 solutions by ewatrrr, Alan3354:Answer by ewatrrr(11158)   (Show Source): You can put this solution on YOUR website! ``` Hi two consecutive negative integers Let x and (x+1) represent the two consecutive 'negative' integers Question states*** x^2 + (x+1)^2 = 41 Solving for x 2x^2 + 2x + 1 = 41 2x^2 + 2x - 40 = 0 x^2 + x - 20 = 0 factoring (x-4)(x+5)= 0 Note:SUM of the inner product(-4x) and the outer product(5x) = x (x-4)=0 x = 4: Extraneous solution, question states 'negative' integers (x+5)= 0 x = -5 The two consecutive 'negative' integers are -5,-4 CHECKING our Answer*** 25 + 16 = 41 ```Answer by Alan3354(34674)   (Show Source): You can put this solution on YOUR website!41/2 = 20.5 apx --> -4 & -5