How do you solve the quadratic equation by completing the square: #x^2+4x-1=0#?

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Answer 1 · 2015-07-21T16:28:47

#color(green)(x = sqrt 5 - 2# or # color(green)(x = -sqrt 5-2#

#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 = 5#

Using the Identity #color(blue)((a+b)^2 = a^2 + 2ab + b^2#, we get
#(x+2)^2 = 5#

#x + 2 = sqrt5# or #x +2 = -sqrt5#

#color(green)(x = sqrt 5 - 2# or # color(green)(x = -sqrt 5-2#