How do you solve using the completing the square method #x^2 + 8x – 2 = 0#?

1 Answer
Shwetank Mauria
Aug 24, 2016

#x=-4-3sqrt2# or #x=-4+3sqrt2#

Explanation:

Compare #x^2+8x-2=0# with the identity #(x+a)^2=x^2+2ax+a^2#. Note that to complete the square we have to add square of half of the coefficient of #x#. As coefficient of x is 8 we should add and subtract #4^2#. Hence,

#x^2+8x-2=0# can be written as

#x^2+8x+16-16-2=0# or

#(x+4)^2-18=0# or

#(x+4)^2-(sqrt18)^2=0# or

#(x+4)^2-(3sqrt2)^2=0# or

#(x+4+3sqrt2)(x+4-3sqrt2)=0# or

#x=-4-3sqrt2# or #x=-4+3sqrt2#

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