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

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Answer 1 · 2016-09-09T15:10:00

#x=-1-2i# or #x=-1+2i#

#x^2+2x+5=0#

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

or #x^2+2xx x xx1+1^2-(-4)=0#

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

Now using identity #a^2-b^2=(a+b)(a-b)#, this becomes

#(x+1+2i)(x+1-2i)=0#

i.e either #x+1+2i=0# and #x=-1-2i#

or #x+1-2i=0# and #x=-1+2i#