The product of two consecutive even numbers is 5624. What are the numbers

Question

vocaloid · Answer

let the first number be 2x
let the second number be 2x + 2

then solve

2x(2x+2) = 5624

solve for x

vocaloid · Answer

let me know if you need help

juju · Answer

O need help

juju · Answer

I need help

thesmartone · Answer

mhmm, vocaloid, why did you use 2x instead of just x?

One number is x, the other even consective number is x + 2

Their product is 5624

x(x+2) = 5624

Now to solve for x, you'll need to distribute the x and then subtract 5624 and solve for the quadratic equation

vocaloid · Answer

@Juju 

do you understand the distributive property?

thesmartone · Answer

But Juju, Vocaloid showed you how to set it up. What didn't you understand?

thesmartone · Answer

And I'll let vocaloid take over, since two people helping will confuse the asker double ;P

juju · Answer

I do not understand the distributive property

juju · Answer

I'm not hearing from vocaloid

mathstudent55 · Answer

@TheSmartOne
The reason for using 2x is that if you let x equal an integers, then 2x must be an even number. Since the problem specifies the numbers are even, then 2x ensures you are dealing with an even number.
2x(2x + 2) = 5624 will give 2 values of x.
That is not your answer.
Then you need to multiply x by 2 to find one even number, and also calculate 2x + 2 to find the second number.

Now we can ask if it is really necessary to use 2x, or if x would be enough, in this problem.
If two integers have an even product, they may be two even numbers or an even number and an odd number. Two odd numbers always have an odd product.
If you just let the smaller number be x, then the larger number will be x + 2.
In this case, just allowing x to represent one of the numbers is also correct.
When you find x, x must be even because if x is odd, then x + 2 is also odd, and their product cannot be even. If x comes out odd, then there is no solution to the question asked.
The problem could have been stated "The product of two consecutive numbers is 5624. Find the numbers."

thesmartone · Answer

Oh, that really cleared it up. Thanks a lot! :)