Question 478485
Let x = the first even number
 x + 2= the second even number

x^2 + (x+2)^2 = 100
x^2 + x^2 + 4x +4 = 100
2x^2 + 4x -96 = 0
Divide by 2 to get
x^2 + 2x -48 = 0
Solve for x by factoring
(x-6)(x+8)= 0
 x = 6
x+2 = 8

The two consecutive even numbers are 6 and 8.

To check
6*6 + 8*8 = 36 + 64 = 100