How do you solve using completing the square method #x^2-6x-7=0#?

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Answer 1 · 2016-05-03T11:56:08

The solutions are:
#color(green)(x = 7# , # color(green)(x = -1#

#x^2 - 6x - 7 =0#

#x^2 - 6x = 7#

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

#x^2 - 6x + color(blue)(9) = 7 + color(blue)(9#

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

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

#(x- 3 )^2 = 16#

#x - 3 = sqrt16# or #x - 3 = -sqrt16#

#x - 3 = 4# or #x - 3 = -4#

#x = 4 + 3 # or #x = -4 + 3 #

#color(green)(x = 7# , # color(green)(x = -1#