How do you solve using the completing the square method #x^2 - 4x - 9 = 0#?

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Answer 1 · 2016-03-30T16:46:55

The solutions are:
#color(green)(x = sqrt 13 + 2# or # color(green)(x = -sqrt 13 + 2#

#x^2 - 4x - 9 =0#

#x^2 - 4x = 9 #

To write the Left Hand Side as a Perfect Square, we add 4 to both sides:

#x^2 - 4x+ 4 = 9 + 4#

#x^2 - 2* x * 2 + 2^2 = 13#

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

#(x-2)^2 = 13#

#x - 2 = sqrt13# or #x -2 = -sqrt13#

#color(green)(x = sqrt 13 + 2# or # color(green)(x = -sqrt 13 + 2#