bear in mind that, if you multiply any integer, by 2, you always get an EVEN number, no matter whatsoever what that integer is. Say 2*2 = even, 17*2= even, 37*2 = even and so on.
So, let's pick a reference integer, say "a", so, 2 * a, we know is an EVEN integer, so our first integer is 2a then.
Now, to get a consecutive integer from any even integer, all you do is, hop backwards one spot, or forwards one spot, like say, 2 + 2, or 2-2, or 6 + 2, or 6 -2 and so on.
Therefore, since our first even integer is 2a, then the next one can just be say, 2a + 2.
Now, we know their product is 440, thus
[tex]\bf (2a)(2a+2)=440\implies 4a^2+4a=440\implies 4(a^2+a)=440
\\\\\\
a^2+a=110\implies a^2+a-110=0\implies (a+11)(a-10)=0
\\\\\\
a=
\begin{cases}
-11\\
\boxed{10}
\end{cases}[/tex]
so.. recall that "a" was only our reference integer, so the even number integers are then 2a and 2a + 2, or 2(10) and 2(10) + 2.
