Question 142875
See this --> http://www.sosmath.com/algebra/quadraticeq/complsquare/complsquare.html

Given : {{{t^2+14t+c}}}
You can see from the sign of the middle term, the answer must be a sum of squares. Also note the leading coefficient is 1. 

Using the equation in the link above, we have
{{{2* sqrt(c) = 14}}}
{{{sqrt(c) = 7}}}
{{{c = 49}}}

Check the answer.
{{{t^2 + 14t + 49}}}
{{{(t+7)^2}}}