Question 1014684
Solve using factoring, completing the square, or the quadratic formula.
{{{s^2+3s+5}}}
Enter the exact answers in increasing order.
using method of completing the square
{{{s^2+3s+5= 0}}}
{{{s^2+3s}}}= -5
add {{{(3/2)^2}}} to both sides
{{{s^2+3s+(3/2)^2}}} = {{{-5+(3/2)^2}}}
{{{s^2+3s+(3/2)^2}}} = -5 + {{{9/4}}}
{{{s^2+3s+(3/2)^2}}} = {{{-11/4}}}
{{{(s+3/2)^2}}} = {{{-11/4}}}
{{{s+3/2}}} = +- {{{sqrt(-11/4)}}}
{{{s+3/2}}} = +- {{{sqrt(-11)/2}}}
since {{{sqrt(-1)}}} = i
{{{s+3/2}}} = +- {{{(i*sqrt(11))/2}}}
s = {{{-(i*sqrt(11))/2 - (3/2)}}} or {{{(i*sqrt(11))/2 - 3/2}}}  
s = {{{-(i*sqrt(11)+3)/2}}} or {{{(i*sqrt(11)- 3)/2}}}