You start with

    x^2 + 6x + 7 = 0


The term 6x says you that the expected square term should be {x+3)^2 = x^2 + 6x + 9


So we add 2 to both sides

    x^2 + 6x + 7 + 2 = 2,   or

    x^2 + 6x + 9 = 2.


In the left side you just have the desired square:

    {x + 3)^2 = 2.


Now take the square root from both sides

    x + 3 = +/- 


Your last step is to move 3 from the left side to the right, changing the sign

    x = -3 +/- .


The problem is just solved.


ANSWER.  The given equation has two roots  x = -3 +   and  x = -3 - .