The product of two consecutive even integers is 168. Find the integers.?

Answer 1

Suppose x is the first even integer.
That makes the next consecutive one x+2

Since their product is 168, that gives us the following equation
(x+2)x = 168

Bring everything to one side so we can find roots
x^2 + 2x = 168
x^2+2x - 168 = 0

Which we can factor and find the roots
(x-12)(x+14) = 0

Have two choices for our x
If we choose x = 12, x+2 = 14
12 and 14 12*14 = 168, so we're good

If we choose x = -14, x+2 = -12
-14 and -12 -12*-14 = 168

so 12,14 or -14,-12

Answer 2

Consecutive even integers are always two numbers apart. It doesn't matter which two you pick, if they are consecutive even they must have a difference of 2 (28, 30 996, 998 and so on)

Therefore if the first integer is x, then we know the next even consecutive integer must be x+2. Product means multiplication and whenever you see the word IS in a word problem, you can conclude that means equals.

From that, we can develop the equation
x(x+2)=168
multiplying through gives us x^2+2x=168
Now that we have a quadratic equation, we can take a few approaches. We can bring the 168 over to the left so that it is equal to zero and try to factor it or we can just complete the square and take it from there. On first glance, it doesn't look like something that is easily factorable and if you are familiar with completing the square, the basic concept is to take half of the coefficient of x and square it to give you the number to add to both sides. In this case 2/2=1^2 which is still just 1.
So now we have x^2+2x+1=169. That turned out great actually because the square root of 169 is a perfect square (13).

From here:
(x+1)^2= 169
sqrt[(x+1)^2=sqrt(169)
x+1= +/- 13
therefore x equals either 12 or -14
That is just the first of the two integers. The second integer would be either 14 or -12

Two possible solutions to this problem:
12, 14 or -14, -12
does 12(12+2) =? 168
12*14=168 so this solution is correct
does -14(-14+2)=? 168
yes that solution is also correct

Answer 3

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The product of two consecutive even integers is 168. Find the integers.?

Answer 4

12 14