SOLUTION: find two consecutive even numbers if the sum of their squares is 100

Question 478487:
find two consecutive even numbers if the sum of their squares is 100

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
an even number is one that is divisible by 2.
let x be the first even number.
let x + 2 be the second even number.
the sum of their squares = 100 means:
x^2 + (x+2)^2 = 100
expand this equation to get:
x^2 + x^2 + 4x + 4 = 100
combine like terms to get:
2x^2 + 4x + 4 = 100
divide both sides of the equation by 2 to get:
x^2 + 2x + 2 = 50
subtract 100 from both sides of the equation to get:
x^2 + 2x - 48 = 0
factor this quadratic equation to get:
(x+8) * (x-6) = 0
solve for x to get:
x = -8 or x = 6
if x = -8, then x+2 = -6
if x = 6, then x+2 = 8
in both cases, plugging those answers into he original equation will show that those values are good.
when x = -8 and x+2 = -6, we get:
64 + 36 = 100
when x = 6 and x+2 = 8, we get:
36 + 64 = 100

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