I assume you mean,
X2 + 12X - 5 = 0
X2 + 12X = 5
Now, halve the linear term (12), square it and add it to both sides
X2 + 12X + 36 = 5 + 36
factor on the left, gather terms on the right
(X + 6)2 = 41
(X + 6)2 - 41 = 0
==============vertex form.... (- 6, - 41)
========================--------------vertex
And that number added is 36
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You must add 36 to complete the square on the left hand side.You must add 36 to complete the square on the left hand side.You must add 36 to complete the square on the left hand side.You must add 36 to complete the square on the left hand side.
The constant term - the part without a variable - must be equal to the square of one half the linear term - the number in front of the "x". That is, it must be (12/2)2 = 36.
36.1. You take the coefficient of x : = 122. Halve it : = 63. Then square it : = 364. Add it.This gives x2 + 12x + 36 = (x + 6)2The above method only works if the coefficient of x2 is 1. If it is not then the processs is slightly more complicated.
x2 + 12x - 11 = x2 + 12x + (12/2)2 - (12/2)2 - 11 = (x + 6)2 - 47
There is no answer to this problem unless x is 0. For the suare root of 98x to be a real number, x has to be positive or zero. For the square root of -147x to be a real number, x has to be negative or zero. Seeing has x has to fit both requirements, the problem has an answer only if x is zero.