Find two consecutive positive even numbers the sum of whose squares is 340

Consecutive even means

x and x+2 since they are 2 apart

sum of squares is 340

x^2 + (x+2) ^2=340

expand and add

x^2+x^2+4x+4=340

2x^2+4x+4=340

divide both sides by 2 to make it easier

x^2+2x+2=170

minus 170 bot sides

x^2+2x-168=0

facotr

(x-12) (x+14) = 0

set each to zero

x-12=0

add 12

x=12

x+14=0

minus 14

x=-14

but they has to e positive to disregard

x=12

x+2=14

numbers are 12 and 14