Two consecutive integers

The product of two consecutive integers is 44 more than 14 times their sum. Find all such integers.

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x = first integer
x + 1 = second integer {consecutive integers increase by 1} 

x(x + 1) = 14(x + x + 1) + 44   {the product of the two is 44 more than 14 times their sum}
x² + x = 14(2x + 1) + 44   {used distributive property and combined like terms}
x² + x = 28x + 14 + 44   {used distributive property}
x² + x = 28x + 58   {combined like terms}
x² - 27x - 58 = 0   {subtracted 28x and 58 from each side}
(x - 29)(x + 2) = 0   {factored into two binomials}
x - 29 = 0 or x + 2 = 0   {set each factor equal to 0}
x = 29 or x = -2   {solved each equation for x}
x + 1 = 30 or x + 1 = -1   {substituted 29 and -2, in for x, into x + 1} 

The two consecutive integers could be 29 and 30 or -2 and -1.


- Algebra House