One number is 6 more than another. The difference between their squares is 120. What are the numbers?
Let x be the first number and x + 6 be the second .....so we have....
(x + 6)2 - x2 = 120 expand and rearrange
x2 + 12x + 36 - x2 - 120 = 0 simplify
12x + 36 = 120 subtract 36 from each side
12x = 84 divide both sides by 12
x = 7 and x + 6 = 13
