What number must you add to complete the square

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What number must you add to complete the square 

x2 +16x=3

Dec 7th, 2014

In order to complete the square you have to consider that the third term of a perfect square should equal (b/2)^2 >> that is the the square of half the value of b, where b is the coeffiecient of the second term. 
So, 
(b/2)^2 = (16/2)^2 = (8)^2 = 64 
The perfect match for the third term is 64 
x2 + 16x = 3 
You have to add 64 on both sides of the equation just to maintain equality, 
x2 + 16x + 64= 3 + 64 
x2 + 16x + 64 = 67 
( x + 8)^2 = 67 
Then it is easier to factorize and find values of x, 
take the square root from both sides, 
(x + 8) = sqrt(67) 
sqrt(67) = 8.18 
1) x = 8.18 - 8 = 0.18 
2) x = -8.18 - 8 = -16.18

Dec 7th, 2014

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