Answer:
36
Explanation:
You want a number c so that x² -12x +c is a perfect square trinomial.
Square
It is helpful to understand the form of the square of a binomial:
(x -a)² = x² -2ax +a²
In this problem, you are given the coefficient of x is 12, and you are asked for the constant corresponding to a².
Application
When we match coefficients, we find the coefficients of x to be ...
-12 = -2a
Dividing by -2 gives ...
6 = a
Then the square we're looking for (a²) is ...
a² = 6² = 36
The trinomial ...
x² -12x +36 = (x -6)²
is a perfect square trinomial.
The constant we want to add is 36.
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Additional comment
We chose to expand the square (x -a)² = x² -2ax +a² so the sign of the x-term would match what you are given. For the purpose of completing the square, that is not important. The added constant is the square of half the x-coefficient. The sign is irrelevant, as the square is always positive.
You will note that when we write the expression as the square of a binomial, the constant in the binomial is half the x-coefficient (and has the same sign).
x² -12x +36 ⇔ (x -6)²