How do you solve using the completing the square method #x^2 - 8x - 3 = 0#?

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Answer 1 · 2016-03-23T17:09:45

The solutions are:
#color(green)(x = sqrt 19 + 4#
# color(green)(x = -sqrt 19 + 4#

#x^2 - 8x - 3 = 0#

#x^2 - 8x = 3#

To write the Left Hand Side as a Perfect Square, we add 16 to both sides:

#x^2 - 8x + 16 = 3 + 16#

#x^2 - 2 * x * 4 + 4^2 = 19 #

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

#(x-4)^2 = 19#

#x - 4 = sqrt19# or #x -4 = -sqrt19#

#color(green)(x = sqrt 19 + 4# or # color(green)(x = -sqrt 19 + 4#