${s}^{2}+2s=6$
To complete the square, the same value needs to be added to both sides${s}^{2}+2s+?=6+?$
To complete the square ${s}^{2}+2s+1={\left( s+1 \right)}^{2}$ add $1$ to the expression${s}^{2}+2s+1=6+?$
Since $1$ was added to the left-hand side, also add $1$ to the right-hand side${s}^{2}+2s+1=6+1$
Use ${a}^{2}+2ab+{b}^{2}={\left( a+b \right)}^{2}$ to factor the expression${\left( s+1 \right)}^{2}=6+1$
Add the numbers${\left( s+1 \right)}^{2}=7$
Solve the equation for $s$$\begin{array} { l }s=-\sqrt{ 7 }-1,\\s=\sqrt{ 7 }-1\end{array}$
The equation has $2$ solutions$\begin{align*}&\begin{array} { l }s_1=-\sqrt{ 7 }-1,& s_2=\sqrt{ 7 }-1\end{array} \\&\begin{array} { l }s_1\approx-3.64575,& s_2\approx1.64575\end{array}\end{align*}$