The product of two consecutive positive integers is 29 more than their sum. Find the integers

Question

The product of two consecutive positive integers is 29 more than their sum. Find the integers

Answer 1

x and x+1 are the integers

x(x+1)=29+x+(x+1)

x^2+x=29+2x+1

x^2+x=30+2x

x^2+x-2x-30=0

x^2-x-30=0

factor

(x-6)(x+5)=0

x-6=0

x=6 and x+1=7

6*7=29+6+7

42=29+13

42=42