How do you solve using the completing the square method #x^2+4x+1=0#?

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Answer 1 · 2016-04-17T17:21:19

The solutions are:
#color(green)(x = sqrt 3 - 2# or # color(green)(x = -sqrt 3 - 2#

#x^2 + 4x + 1 = 0 #

#x^2 + 4x = - 1 #

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

#x^2 + 4x + 4 = -1 + 4#

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

Using the Identity #color(blue)((a+b)^2 = a^2 + 2ab + b^2#, we get
#(x+2)^2 = 3#

#x + 2 = sqrt3# or #x + 2 = -sqrt3#

#color(green)(x = sqrt 3 - 2# or # color(green)(x = -sqrt 3 - 2#