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