${x}^{2}+6x=16$
To complete the square, the same value needs to be added to both sides${x}^{2}+6x+?=16+?$
To complete the square ${x}^{2}+6x+9={\left( x+3 \right)}^{2}$ add $9$ to the expression${x}^{2}+6x+9=16+?$
Since $9$ was added to the left-hand side, also add $9$ to the right-hand side${x}^{2}+6x+9=16+9$
Use ${a}^{2}+2ab+{b}^{2}={\left( a+b \right)}^{2}$ to factor the expression${\left( x+3 \right)}^{2}=16+9$
Add the numbers${\left( x+3 \right)}^{2}=25$
Solve the equation for $x$$\begin{array} { l }x=-8,\\x=2\end{array}$
The equation has $2$ solutions$\begin{array} { l }x_1=-8,& x_2=2\end{array}$