Question

How do you solve `y=x^2-12x+36`?

Answer 1

This is a perfect square trinomial:

`x^2-12x+36 = (x-6)^2`

So `y = 0` when `x=6`

Explanation:

Perfect square trinomials are of the form:

`a^2+-2ab+b^2 = (a+-b)^2`

In our case notice that the leading term `x^2` is square and the constant term `36 = 6^2` is square. So the question is: Is the middle term equal to `+-2*x*6 = +-12x` - Yes.