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} The two consecutive integers could be 29 and 30 or 2 and 1.  Algebra House
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