Answer:
[tex]x=-3+\sqrt{3}\text{ or }x=-3-\sqrt{3}[/tex]
Explanation:
The equation is [tex]x^2+6x+6=0[/tex] .
I will complete squares to solve for x.
[tex]\text{Given: }x^2+6x+6=0\\ \\ \text{Subtract 6 from both sides: }x^2+6x=-6\\ \\ \text{Add the square of the half of the coefficient of x to both sides:}\\\\ \text{ }x^2+6x+9=-6+9[/tex]
[tex]\text{Factor the left side and simplify the right side: }(x+3)^2=3[/tex]
[tex]\text{Square root both sides: }x+3=\pm \sqrt{3}[/tex]
[tex]\text{Clear x:}\\ \\ x=-3\pm \sqrt{3}\\\\ x=-3-\sqrt{3}\text{ or }x=-3+\sqrt{3}[/tex]
