Answer:
D and F
Step-by-step explanation:
[tex]x^{2}+4x+4=12[/tex] can be rewritten as [tex]x^{2} +4x-8=0[/tex].
From there you can use the quadratic formula [tex]x=\frac{-b±\sqrt{b^{2}+4ac } }{2a}[/tex] (ignore the A, I can‘t seem to remove it), where a=1, b=4, and c=-8.
[tex]x=\frac{-4±\sqrt{4^{2}-4(1)(-8)} }{2(1)}[/tex]
Then you get [tex]x=\frac{-4±\sqrt{16+32}}{2}[/tex]
Then you get [tex]x=\frac{-4±\sqrt{48} }{2}[/tex]
So [tex]x=-2±\frac{4\sqrt{3} }{2}[/tex]
Which means [tex]x=-2+2\sqrt{3}[/tex] or [tex]-2-2\sqrt{3}[/tex] which are choices D and F.
