Question 933100
That means, Complete The Square.


  You need to FIRST factor the coefficient of 2 from the entire polynomial, AND THEN perform Completion of the Square.   The term will be  {{{(6/2)^2=3^2=9}}}.


{{{2(x^2+6x)}}}, your same expression factored.
;
Now add AND subtract the necessary term, the square missing term.
{{{2(x^2+6x+9-9)}}}
{{{2((x+3)^2-9)}}}
Distribute the factor of 2 which was earlier factored.
{{{highlight(2(x+3)^2-18)}}}



Your expected result of {{{2(x-a)^2+6}}} seems wrong.