How do you solve #9x^2 -18x - 1 =0# by completing the square?

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Answer 1 · 2016-04-06T12:40:54

The solutions are:
#color(green)(x = (sqrt 10 + 3)/3# , # color(green)(x = (-sqrt 10 + 3) / 3#

#9x^2 - 18x - 1 = 0#

#9x^2 - 18x = 1#

To write the Left Hand Side as a Perfect Square, we add 9 to both sides:

#9x^2 - 18x + 9 = 1 + 9 #

#(3x)^2 - 2 * 3x * 3 + 3 ^2 = 10#

Using the Identity #color(blue)((a-b)^2 = a^2 - 2ab + b^2#, we get

#(3x - 3)^2 = 10#

#3x - 3 = sqrt 10# or #3x - 3 = -sqrt10#

#color(green)(x = (sqrt 10 + 3)/3# or # color(green)(x = (-sqrt 10 + 3) / 3#