one number is 2 larger than another number. the sum of their squares is 100. find the numbers

x= first number
x+2= second number

x^2 + (x + 2)^2= 100
square the parentheses

x^2 + [(x + 2)(x + 2)]= 100
x^2 + x^2 + 2x + 2x + 4= 100
combine like terms

2x^2 + 4x + 4= 100
subtract 100 from both sides

2x^2 + 4x - 96= 0
factor

2(x−6)(x+8)=0
set each parentheses equal to 0

x-6= 0
x= 6

OR

x+8= 0
x= -8

CHECK:
x^2 + (x + 2)^2= 100
(6)^2 + (6 + 2)^2= 100
36 + (8)^2= 100
36 + 64= 100
100= 100

x^2 + (x + 2)^2= 100
(-8)^2 + (-8 + 2)^2= 100
64 + (-6)^2= 100
64 + 36= 100
100= 100


ANSWER: x= 6 or x= -8

Hope this helps! :)