First, factor out the 2 from the first two terms:
[tex]2t^2-4t-1=2(t^2-2t)-1[/tex]
To complete the square, we need to add and subtract a term to the grouped term so that it's the result you would get from squaring some binomial. In this case, notice that
[tex](t-1)^2=t^2-2t+1[/tex]
which means we should add and subtract 1 as follows, then condense the quadratic terms:
[tex]2(t^2-2t+1-1)-1=2(t^2-2t+1)-3=2(t-1)^2-3[/tex]
