Answer:
36
Step-by-step explanation:
The expansion of the binomial square ...
(n +a)²
is ...
(n +a)² = n² +2an +a²
__
When we compare this to the given expression ...
n +12n + __
we see that the linear terms can help us find the value of 'a':
12n = 2an . . . match linear term values
6 = a . . . . . . divide by 2n
The constant that goes in the blank is ...
a² = 6² = 36
The perfect square trinomial is ...
n² +12n +36
_____
In short, the value that "completes the square" is the square of half the coefficient of the linear term. (12/2)² = 36.
