$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } = 0$
$ $ Bind the expressions with the common factor $ x$
$\color{#FF6800}{ x } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \right ) = 0$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 4 \pm \sqrt{ 4 ^ { 2 } - 4 \times 1 \times 0 } } { 2 \times 1 } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 4 \pm \sqrt{ 16 } } { 2 \times 1 } }$
$x = \dfrac { - 4 \pm \sqrt{ \color{#FF6800}{ 16 } } } { 2 \times 1 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$x = \dfrac { - 4 \pm \color{#FF6800}{ 4 } } { 2 \times 1 }$
$x = \dfrac { - 4 \pm 4 } { 2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
$ $ Multiplying any number by 1 does not change the value $ $
$x = \dfrac { - 4 \pm 4 } { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 4 \pm 4 } { 2 } }$
$ $ Separate the answer $ $
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 4 + 4 } { 2 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 4 - 4 } { 2 } } \end{array}$
$\begin{array} {l} x = \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } } { 2 } \\ x = \dfrac { - 4 - 4 } { 2 } \end{array}$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$\begin{array} {l} x = \dfrac { 0 } { 2 } \\ x = \dfrac { - 4 - 4 } { 2 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { 0 } { 2 } } \\ x = \dfrac { - 4 - 4 } { 2 } \end{array}$
$ $ If the numerator is 0, it is equal to 0 $ $
$\begin{array} {l} x = \color{#FF6800}{ 0 } \\ x = \dfrac { - 4 - 4 } { 2 } \end{array}$
$\begin{array} {l} x = 0 \\ x = \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } } { 2 } \end{array}$
$ $ Find the sum of the negative numbers $ $
$\begin{array} {l} x = 0 \\ x = \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 8 } } { 2 } \end{array}$
$\begin{array} {l} x = 0 \\ x = \color{#FF6800}{ \dfrac { - 8 } { 2 } } \end{array}$
$ $ Do the reduction of the fraction format $ $
$\begin{array} {l} x = 0 \\ x = \color{#FF6800}{ \dfrac { - 4 } { 1 } } \end{array}$
$\begin{array} {l} x = 0 \\ x = \dfrac { - 4 } { \color{#FF6800}{ 1 } } \end{array}$
$ $ If the denominator is 1, the denominator can be removed $ $
$\begin{array} {l} x = 0 \\ x = \color{#FF6800}{ - } \color{#FF6800}{ 4 } \end{array}$