x² - 6x + 9 = 100

Factor the left side:

    (x-3)(x-3) = 100

Since the two factors are the same we can write the factor just
once with a 2 exponent, that is, as a square of a binomial:

        (x-3)² = 100

Now we use the principle of square roots.  

         x-3 = ±

         x-3 = ±10

Add 3 to both sides

           x = ±10 + 3

Then we make two equations, one using + and one using -

   x = 10 + 3,     x = -10 + 3
   x = 13,         x = -7

Edwin