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x^2 - 10x - 9 = 0
first we will move the constant term to the other side
x^2 - 10x = 9
then, to both sides we will add the number that makes the polynomial on the left a perfect square trinomial. Take half of the coefficient of x, then square it. half of the coefficient of x (-10) is -5, and -5 squared is 25. so:
x^2 - 10x + 25 = 34
factor the perfect square trinomial
(x - 5)^2 = 34
x - 5 = plus or minus sqrt(34)
x = 5 plus or minus sqrt(34)

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