Let's make the first even integer m and the second even integer n. The square of the first, decreased by the second is 130 is:
[tex] m^{2} [/tex]-n=130 ---> Add n to each side
[tex] m^{2} [/tex]=130+n ---> Take the square root of each side
m=±[tex] \sqrt{130+n}[/tex]
Let's look at the first square number above 130, which is [tex] 12^{2}[/tex]. m is 12, therefore the next consecutive even integer is 14.
[tex] 12^{2}[/tex]=144
144-14=130
The two consecutive integers are 12 and 14
