# SOLUTION: The product of two consecutive even integers is 224. Find the integers

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 Question 599451: The product of two consecutive even integers is 224. Find the integersAnswer by Edwin McCravy(8908)   (Show Source): You can put this solution on YOUR website!The product of two consecutive even integers is 224. Find the integers ```I'll show you two ways to do it. One way your teacher won't accept and one that he or she will accept" Here's the easy way that your teacher won't accept. They have to both be close to the square root of 224. So we find the square root of 224 with a calculator and get 14.966629555. So we take the two consecutive even integers that 14.966629555 is between and we get that 14.966629555 is between the two consecutive integers 14 and 16. So they are one of the answers. But another solution is found by taking the negatives of those, -16 and -14, since their product is also +224. Your teacher won't accept this way but it's a good way to know when you've got the right answer. Here's the way your teacher will accept: Let x represent the smaller consecutive even integer Then x + 2 represents the larger consecutive even integer x(x + 2) = 224 x² + 2x = 224 x² + 2x - 224 = 0 (x - 14)(x + 16) = 0 x - 14 = 0; x + 16 = 0 x = 14; x = -16 x+2 = 14 + 2 = 16; x+2 = -16 + 2 = -14; So there are two solutions (14 and 16) and (-16 and -14) Edwin```