<s>[INST] Where did I go wrong in completing the square? $$2x^{ 2 }+8x+1=0$$
Move 1 to the other side of the equation: 
$$2x^{ 2 }+8x\quad =-1$$
Divide both sides by 2 to get 1 as the leading coefficient:
$$x^{ 2 }+4x\quad =-\frac { 1 }{ 2 } $$
$$(\frac { 4 }{ 2 } )^{ 2 }$$
$$x^{ 2 }+4x+4\quad =-\frac { 1 }{ 2 } +4$$
$$(x+2)^{ 2 }=3.5$$
I get to this and it seems to be the wrong answer: 
$$x={ -2 }\pm\sqrt { \frac { 7 }{ 2 }  } $$
 [/INST] Your calculations are right..
$$(x+2)^2=\frac{7}{2} \Rightarrow x+2=\pm \sqrt{\frac{7}{2}} \Rightarrow x=-2 \pm \sqrt{\frac{7}{2}}=-2 \pm \frac{\sqrt{14}}{2}$$
So:
$$x=-2 \pm \frac{\sqrt{14}}{2}$$
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