How do you solve using the completing the square method #x^2-8x+7=0#?

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Answer 1 · 2016-05-06T15:02:56

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

#x^2 - 8x + 7 = 0#

#x^2 - 8x = - 7 #

To write the Left Hand Side as a Perfect Square, we add 16 to both sides
#x^2 - 8x + 16 = - 7 + 16 #

#x^2 - 8x + 16 = 9 #

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

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

#(x-4)^2 = 9#

#x - 4 = sqrt9# or #x -4 = -sqrt9#

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

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

#color(green)(x = 7# or # color(green)(x = 1#