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Verified Answer :

x*(x+2) = 255 
x^2 + 2x = 255 
x^2 + 2x - 255 = 0 

Solve for x: 
(x+15)(x-17)=0 

One solution is x = -17 and (x+2) = -15 
The other solution is x = 15 and (x+2) = 17

(x)(x+2) = 255
x² + 2x - 255 = 0
x² -15x + 17x - 255 = 0
x(x-15) 17(x-15) = 0
(x+17)(x-15) = 0
x = -17 Or x = 15

-17 is rejected 'cause it is negative. So, one number of 15, 
other 15 +2 = 17

In short, Your Numbers are 15 & 17

Hope this helps!

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