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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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Q: What number must you add to complete the square x2 12x -5?
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