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

1 Answer
Shwetank Mauria
Mar 22, 2016

Please follow the process given below. Answer is #x=0# and #x=-2#

Explanation:

We know that #(x+a)^2=x^2+2ax+a^2#, hence to complete say #x^2+bx# to a square we should add and subtract, square of half the coefficient of #x# i.e. #(b/2)^2#.

As the equation is #x^2+2x=0#, we have to add and subtract #(2/2)^2=1# and equation becomes

#x^2+2x+1-1=0# and now this can be written as

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

#((x+1)+1)xx((x+1)-1)=0# or

#((x+2)xx x=0# i.e. either #x=0# or #x+2=0# or #x=-2#

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