Question 696399
No one else knew what you wanted or meant, but I read minds.
 
{{{x^2+4x+2=0}}}
 
Completing the Square:
The square that starts with {{{x^2+4x}}} is
{{{x^2+4x+4=(x+2)^2}}}
Adding {{{2}}} to each side of {{{x^2+4x+2=0}}} we get
{{{x^2+4x+4=2}}} , which we can re-write as
{{{(x+2)^2=2}}}, which means that
either {{{x+2=sqrt(2)}}},
or {{{x+2=-sqrt(2)}}}.
{{{x+2=sqrt(2)}}} means {{{x=-2+sqrt(2)}}}
{{{x+2=-sqrt(2)}}} means {{{x=-2-sqrt(2)}}}
Both values of {{{x}}} are solutions of {{{x^2+4x+2=0}}}.
We can write both solutions as
{{{highlight(x=-2 +- sqrt(2))}}}