The sum of the squares of two consecutive odd positive integers is 130. find the integers

2 consecutive odd positive integersx and x + 2

x^2 + (x + 2)^2 = 130
x^2 + (x + 2)(x + 2) = 130
x^2 + x^2 + 4x + 4 = 130
2x^2 + 4x + 4 = 130
2x^2 + 4x + 4 - 130 = 0
2x^2 + 4x - 126 = 0
2(x^2 + 2x - 63) = 0
2(x - 7)(x + 9) = 0

x - 7 = 0
x = 7

x + 9 = 0
x = -9 (cant be this one because it is negative

so x = 7...and x + 2 = 7 + 2 = 9ur 2 numbers are 7 and 9

1. statement- ca is parallel to db and e is the midpoint of ad reason- given2. statement- reason- alternate interior angles3. statement- de is congruent to ae reason- definition of midpoint4. statement- triangle aec is congruent to triangle deb reason- asa (angle side angle)