The product of two consecutive positive even integers is 224. Find the two integers.
x = first even integer
x + 2 = second even integer {even integers increase by 2} x(x + 2) = 224 {the product of two consecutive positive even integers is 224} x² + 2x = 224 {used distributive property} x² + 2x  224 = 0 {subtracted 224 from each side} (x + 16)(x  14) = 0 {factored into two binomials} x + 16 = 0 or x  14 = 0 {set each factor equal to zero} x = 16 or x = 14 {solved each equation} x = 14 {only the positive even integer} x + 2 = 16 {substituted 14, in for x, into x + 2} 14 and 16 are the two consecutive positive even integers Ask the House
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January 2021
