$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } = \color{#FF6800}{ 0 }$
$ $ Solve the quadratic equation $ ax^{2}+bx+c=0 $ using the quadratic formula $ \dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } }$
$x = \dfrac { \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 4 \right ) \pm \sqrt{ \left ( - 4 \right ) ^ { 2 } - 4 \times 1 \times 1 } } { 2 \times 1 }$
$ $ Simplify Minus $ $
$x = \dfrac { 4 \pm \sqrt{ \left ( - 4 \right ) ^ { 2 } - 4 \times 1 \times 1 } } { 2 \times 1 }$
$x = \dfrac { 4 \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \right ) ^ { \color{#FF6800}{ 2 } } - 4 \times 1 \times 1 } } { 2 \times 1 }$
$ $ Remove negative signs because negative numbers raised to even powers are positive $ $
$x = \dfrac { 4 \pm \sqrt{ 4 ^ { 2 } - 4 \times 1 \times 1 } } { 2 \times 1 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } \pm \sqrt{ \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } \pm \sqrt{ \color{#FF6800}{ 12 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } }$
$x = \dfrac { 4 \pm \sqrt{ \color{#FF6800}{ 12 } } } { 2 \times 1 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$x = \dfrac { 4 \pm \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } } { 2 \times 1 }$
$x = \dfrac { 4 \pm 2 \sqrt{ 3 } } { 2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
$ $ Multiplying any number by 1 does not change the value $ $
$x = \dfrac { 4 \pm 2 \sqrt{ 3 } } { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } \pm \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 2 } } }$
$ $ Separate the answer $ $
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 2 } } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 2 } } } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 2 } } } \\ x = \dfrac { 4 - 2 \sqrt{ 3 } } { 2 } \end{array}$
$ $ Do the reduction of the fraction format $ $
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 1 } } } \\ x = \dfrac { 4 - 2 \sqrt{ 3 } } { 2 } \end{array}$
$\begin{array} {l} x = \dfrac { 2 + \sqrt{ 3 } } { \color{#FF6800}{ 1 } } \\ x = \dfrac { 4 - 2 \sqrt{ 3 } } { 2 } \end{array}$
$ $ If the denominator is 1, the denominator can be removed $ $
$\begin{array} {l} x = \color{#FF6800}{ 2 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 3 } } \\ x = \dfrac { 4 - 2 \sqrt{ 3 } } { 2 } \end{array}$
$\begin{array} {l} x = 2 + \sqrt{ 3 } \\ x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 2 } } } \end{array}$
$ $ Do the reduction of the fraction format $ $
$\begin{array} {l} x = 2 + \sqrt{ 3 } \\ x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } } { \color{#FF6800}{ 1 } } } \end{array}$
$\begin{array} {l} x = 2 + \sqrt{ 3 } \\ x = \dfrac { 2 - \sqrt{ 3 } } { \color{#FF6800}{ 1 } } \end{array}$
$ $ If the denominator is 1, the denominator can be removed $ $
$\begin{array} {l} x = 2 + \sqrt{ 3 } \\ x = \color{#FF6800}{ 2 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 3 } } \end{array}$