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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