A positive integer squared plus 2 times it’s consecutive integer is equal to 82. Find the integer.

Answer 1

x^2 +2(x+1) = 82

x^2 +2x +2 = 82

x^2 +2x = 80

x^2 +2x + 1 = 80+1

(x+1)^2 = 81

x+1 = + or -sqr81 = 9 or -9

x =8 or -10

64 + 16 = 80

100-20 = 80

but you only want the positive integers: 8 and 9