How do you solve using the completing the square method #x^2-2x-5=0#?

1 Answer
Feb 25, 2016

Answer:

#(1-sqrt6)# and #(1+sqrt6)#

Explanation:

To solve #x^2−2x−5=0# using the completing the square method, one picks up terms containing #x^2# and #x#. Here these are #x^2−2x#. Here coefficient of #x^2# is one and that of #x# is #-2#, hence adding half of the square of latter i.e. adding #(-1)^2# (i..e. #1#) should make #x^2−2x#, a complete square.

Hence for solving, let us add and subtract #1#, and doing this the equation becomes

#x^2−2x+1−6=0#

or #(x-1)^2-(sqrt6)^2=0#

i.e. #(x-1+sqrt6)(x-1-sqrt6)=0#

i.e. #x=(1-sqrt6)# or #x=(1+sqrt6)#