Answer
$x=-2-\sqrt 3,-2+\sqrt 3$
Work Step by Step
To complete the square, add a term that is the square of half the coefficient of $x$ to both sides of the equation, and factor the left side. Then use the square root property to simplify both sides, and then isolate $x$.
$x^2+4x+1=0$
$(\frac{4}{2})^2=(2)^2$
$x^2+4x+1-1+(2)^2=-1+(2)^2$
$x^2+4x+(2)^2=-1+(2)^2$
$x^2+4x+4=-1+4$
$x^2+4x+4=3$
$(x+2)^2=3$
$x+2=±\sqrt 3$
$x=-2±\sqrt 3$
$x=-2-\sqrt 3,-2+\sqrt 3$
