SOLUTION: find two consequetive even integers whose product equal 120

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Question 280358: find two consequetive even integers whose product equal 120
Found 2 solutions by Alan3354, jsmallt9:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(120) = about 11, between the 2 numbers.
--> 10 & 12 or -12 & -10

Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the first even integer. Then x+2 = the second even integer. Their product would be x(x+2). This is 120:
x%28x%2B2%29+=+120
Now we solve for x. Start by simplifying the left side:
x%5E2%2B2x+=+120
Since this is a quadratic equation we want one side to be zero. So subtract 120 from each side:
x%5E2%2B2x+-+120+=+0
Now we factor (or use the Quadratic Formula):
%28x%2B12%29%28x-10%29+=+0
By the Zero Product Property we know that one of these factors must be zero:
x+12 = 0 or x-10 = 0
Solving these we get:
x = -12 or x = 10
That make the second even integer...
x+2 = -12 + 2 = -10 or x+2 = 10 + 2 = 12

So there are two pairs of consecutive even integers whose product is 120:
-12 and -10 or 10 and 12