The product of two consecutive, positive, even integers

​The product of two consecutive positive even integers is 224. Find the two integers.

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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

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