x2-12x+36 = (x-6)2
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x2 + 12x - 11 = x2 + 12x + (12/2)2 - (12/2)2 - 11 = (x + 6)2 - 47
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.
-2x3 + 2x2 + 12x =(-2x) (x2 - x - 6) =(-2x) (x+2) (x-3)
I assume you mean,X2 + 12X - 5 = 0X2 + 12X = 5Now, halve the linear term (12), square it and add it to both sidesX2 + 12X + 36 = 5 + 36factor on the left, gather terms on the right(X + 6)2 = 41(X + 6)2 - 41 = 0==============vertex form.... (- 6, - 41)========================--------------vertexAnd that number added is 36
if x2 + 7 = 37, then x2 = 29 and x = ±√29