What number needs to be added to both sides of the equation in order to complete the square?

16

Step-by-step explanation:

Given x^2 + 16x = 18.  Complete the square:

Take half of the coefficient of x (in other words, take half of 16) and square the result:  we get 8^2 = 64.

Add 64, and then subtract 64 from x^2 + 16x   + 64                         = 18 + 64

Then (x + 8)^2  = 82.  From this point on it's easy to find the roots, but we were not asked to do so.  

The desired number is 64; note that it is (16/2)^2.

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