One positive number is 8 more than another. The sum of their squares is 130. Find both numbers

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