Evaluate: s^2+2s-6=0

Expression: ${s}^{2}+2s-6=0$

Move the constant to the right-hand side and change its sign

${s}^{2}+2s=6$

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

$\begin{align*}&\begin{array} { l }s_1=-\sqrt{ 7 }-1,& s_2=\sqrt{ 7 }-1\end{array} \\&\begin{array} { l }s_1\approx-3.64575,& s_2\approx1.64575\end{array}\end{align*}$