Use a special product formula to factor the perfect square trinomial.?

Question

36 x^2 - 72 x + 36.

I have the book in front of me. I still don't understand

Answer 1

In a perfect square trinomial the middle term ("x" term) is twice the product of the two terms in the factors (ax+b)^2 = a^2x^2 +2*a*b*x+ b^2. So if the trinomial is cx^2 + dx + e, a=√c, b=√e. So a = ±6, and b = ±6. You have to decide whether they are both + or -; since 2*a*b= -72, so a*b = -36 so the factors must be (6x - 6)*(6x - 6).

EDIT: Naturally to complete the factorization, you would separate the constant factor in each term: 6*(x-1)*6*(x-1) = 36*(x-1)*(x-1); I left it in at the start to illustrate the general approach to perfect-square trinomials.

Answer 2

36(x^2-2x+1)=0
36(x-1)(x-1)=0

First you factor out the greatest common factor which in this case is 36 then you end up with simplified form then after you will try to factor it. Usually you guess and check. But after a while you can figure out the solution by just looking at it.
The answer is x= 1