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

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}

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*