Consecutive even integers problem

[gcooper]

The sum of the squares of two consecutive even integers is 164. Find the integers.

Here's how I tried to do it(using the zero theorem):

x^2 + x^2 + 2^2 = 164
2x^2 + 4 = 164
2x^2 + 4 - 164 = 0

Now, I tried to find 2 numbers that multiply to 328 and add to 4, but I couldn't, so I'm now stuck. I'm sure I'm doing a mistake somewhere in the process, but where?

 

[HallsofIvy]

Here is your error: (x+ 2)^2 is NOT x^2+ 2^2.

If one even number is "x", then the next even number is "x+ 2" but the sum of the squares is
x^2+ (x+ 2)^2= x^2+ (x^2+ 4x+ 4)= 2x^2+ 4x+ 4= 164

You want to solve 2x^2+ 4x- 160= 0 which is the same x^2+ 2x- 80= 0.

 

[gcooper]

thank you very much for the help, now i see my error