Calculate: x^2+6x-16=0

Expression: ${x}^{2}+6x-16=0$

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

${x}^{2}+6x=16$

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

$\begin{array} { l }x_1=-8,& x_2=2\end{array}$