Question 754841
{{{s^2+5s+1=0}}}
You want to know what square term to add and subtract.
That term is {{{(5/2)^2=25/4}}}.
{{{s^2+5s+25/4+1-25/4=0}}}
Showing which part is the square trinomial,
{{{(s^2+5s+25/4)+1-25/4=0}}}
{{{(s+5/2)^2+4/4-25/4=0}}}
{{{(s+5/2)^2-21/4=0}}}


You should have no trouble solving for s from there.


{{{(s+5/2)^2=21/4}}}
{{{s+5/2=+- sqrt(21)/2}}}______without the tags, I say 5/2 plus-or-minus (1/2)*(21)^(0.5)
{{{highlight(s=(-5+- sqrt(21))/2)}}}