X^2  2X  8 = 0
a = 1 b = 2 c= 8
put in the form (x+b/2a)^{2 }and keep the balance
(x2/2)^{2}1  8 =0
(x  1)^{2}=9
x 1 = 3 or x 1 = 3
x = 3 + 1 or x = 3 + 1
x = 4, x = 2
previous solution is correct hopefully this explained where the added 1 came from and how to determine what constant to use to keep the balance of the equation.
x^214x3=0
a = 1 b = 14
(x14/2)^{2 }=x^{2}14x +49
since you added 49 on the left then add to the right to keep the balance
(x  7)² =0 + 49 + 3 = 52
x  7 = √52
x = 7 + √52 or 7  √52
5/26/2014

PAT T.