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

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Answer 1 · 2016-03-07T05:25:12

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

Given equation is #x^2-4x+1=0#

#x^2-4x=-1#--------(1)

#third term =(1/2 xx # coefficient of x #)^2#

#third term = (1/2xx -4)^2#

#third term = (-2)^2#

#third term =4#

Add 4 to both sides of equation 1

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

#(x-2)^2 = 3#

#(x-2)= +- sqrt3#

#x=2+-sqrt3#

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