X2 - 8X = 3
halve the linear term (- 8 ), square it and add it to both sides
X2 - 8X + 16 = 3 + 16
factor left, gather terms right
(X - 4)2 = 19
(X - 4)2 - 19 = 0
-------------------------
(4, - 19)
----------------the vertex
16 is the number that needed to be added to both sides to complete the square
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You must add (17n + 144).
If: x^2 +18x = 29 Then completing the square: (x+9)^2 -81 = 29 or (x+9)^2 = 110
144
Adding 100 completes the square. { I wonder why you want to complete the square when the expression already factors as x(x-20) }.
49 x2 + 14x = -7 x2 + 14x + 49 = 42 (x + 7)2 = 42 x = -7 ± √42