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

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Answer 1 · 2016-03-31T17:29:56

The solutions are:
#color(green)(x = 2# ,
# color(green)(x = -4#

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

#x^2 + 2x = 8#

To write the Left Hand Side as a Perfect Square, we add 1 to both sides:

#x^2 + 2x + 1 = 8 + 1#

#x^2 + 2* x * 1 + 1 = 9#

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

#(x+1)^2 = 9#

#x + 1 = sqrt9# or #x + 1 = -sqrt9#

#color(green)(x = 3 -1 = 2# or # color(green)(x = -3 - 1 = -4#