first number: x
second number: x + 8
(x)² + (x + 8)² = 130
x² + x² + 16x + 64 = 130
2x² + 16x + 64 = 130
x² + 8x + 32 = 65 divided both sides by 2
x² + 8x - 33 = 0 subtracted 65 from both sides
(x + 11)(x - 3) = 0
x + 11 = 0 x - 3 = 0
x = -11 x = 3 disregard -11 because it's not a positive number
second number: x + 8 = (3) + 8 = 11
Answer: 3 and 11
