Number Word Problem

The product of two numbers is 323 and the difference between them is 2.  What are the two numbers?

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x = one number
y = other number

xy = 323   {product of two numbers is 323}
x - y = 2   {difference between the two numbers is 2}

x = y + 2   {re-arranged second equation}

(y + 2)(y) = 323   {substituted (y + 2), in for x, into top equation}
y² + 2y = 323   {used distributive property}
y² + 2y - 323 = 0   {subtracted 323 from each side}
(y + 19)(y - 17) = 0   {factored into two binomials}
y + 19 = 0   or   y - 17 = 0   {set each factor equal to 0}
y = -19   or   y = 17   {solved each equation for y}

x = y + 2   {bottom re-arranged equation}
x = -19 + 2    or    x = 17 + 2   {substituted -19 and 17, in for y, into bottom re-arranged equation}
x = -17   or   x = 19   {solved each equation for x}

-17 and -19
        or
 19 and 17    
could be the two numbers

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