SOLUTION: The sum of two consecutive even integers is ten less than twice their product. Find their integers using factoring.

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Question 167159: The sum of two consecutive even integers is ten less than twice their product. Find their integers using factoring.
Answer by nerdybill(7384) About Me  (Show Source):
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The sum of two consecutive even integers is ten less than twice their product. Find their integers using factoring.
.
Let x = 1st consecutive even integers
then
x+2 = 2nd consecutive even integers
.
x + x+2 = 2(x)(x+2) -10
2x+2 = 2x(x+2) -10
2x+2 = 4x^2+4x -10
2 = 4x^2+2x-10
0 = 4x^2+2x-12
0 = 2x^2+x-6
.
0 = (2x-3)(x+2)
.
Setting each to zero:
2x-3 = 0
2x = 3
x = 3/2
.
x+2 = 0
x = -2
.
Solution: x = {-2, 3/2}