Question 629623
To solve for k, lets complete the square.
Add (b/2a)^2 to each side: 
k^2+5k+(5/4)^2= 2+(5/4)^2
k^2+5k+25/16= 57/16
Factor:
(k+5/4)^2= 57/16
Take the square root of each side:
{{{k+5/4= sqrt(57)/(4)}}}
Subtract 5/4 from each side to find k:
{{{k= sqrt(57)/(4)-5/(4)}}}