$x ^ { 2 } = \color{#FF6800}{ \dfrac { \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \right ) } { \color{#FF6800}{ 3 } } }$
$ $ Arrange the fraction expression $ $
$x ^ { 2 } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } { \color{#FF6800}{ 3 } } }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } { \color{#FF6800}{ 3 } } }$
$ $ Multiply both sides by the least common multiple for the denominators to eliminate the fraction $ $
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
$3 x ^ { 2 } = \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ x } + 2$
$ $ Move the expression to the left side and change the symbol $ $
$3 x ^ { 2 } - x ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } = 0$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } - 3 x - 2 = 0$
$ $ Calculate between similar terms $ $
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } - 3 x - 2 = 0$
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } = \color{#FF6800}{ 0 }$
$ $ Solve the quadratic equation $ ax^{2}+bx+c=0 $ using the quadratic formula $ \dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } }$
$x = \dfrac { \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 3 \right ) \pm \sqrt{ \left ( - 3 \right ) ^ { 2 } - 4 \times 2 \times \left ( - 2 \right ) } } { 2 \times 2 }$
$ $ Simplify Minus $ $
$x = \dfrac { 3 \pm \sqrt{ \left ( - 3 \right ) ^ { 2 } - 4 \times 2 \times \left ( - 2 \right ) } } { 2 \times 2 }$
$x = \dfrac { 3 \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) ^ { \color{#FF6800}{ 2 } } - 4 \times 2 \times \left ( - 2 \right ) } } { 2 \times 2 }$
$ $ Remove negative signs because negative numbers raised to even powers are positive $ $
$x = \dfrac { 3 \pm \sqrt{ 3 ^ { 2 } - 4 \times 2 \times \left ( - 2 \right ) } } { 2 \times 2 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \pm \sqrt{ \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \pm \sqrt{ \color{#FF6800}{ 25 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } } }$
$x = \dfrac { 3 \pm \sqrt{ \color{#FF6800}{ 25 } } } { 2 \times 2 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$x = \dfrac { 3 \pm \color{#FF6800}{ 5 } } { 2 \times 2 }$
$x = \dfrac { 3 \pm 5 } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 2 } }$
$ $ Multiply $ 2 $ and $ 2$
$x = \dfrac { 3 \pm 5 } { \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \pm \color{#FF6800}{ 5 } } { \color{#FF6800}{ 4 } } }$
$ $ Separate the answer $ $
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } } { \color{#FF6800}{ 4 } } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } } { \color{#FF6800}{ 4 } } } \end{array}$
$\begin{array} {l} x = \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } } { 4 } \\ x = \dfrac { 3 - 5 } { 4 } \end{array}$
$ $ Add $ 3 $ and $ 5$
$\begin{array} {l} x = \dfrac { \color{#FF6800}{ 8 } } { 4 } \\ x = \dfrac { 3 - 5 } { 4 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 8 } } { \color{#FF6800}{ 4 } } } \\ x = \dfrac { 3 - 5 } { 4 } \end{array}$
$ $ Do the reduction of the fraction format $ $
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 1 } } } \\ x = \dfrac { 3 - 5 } { 4 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 1 } } } \\ x = \dfrac { 3 - 5 } { 4 } \end{array}$
$ $ Reduce the fraction to the lowest term $ $
$\begin{array} {l} x = \color{#FF6800}{ 2 } \\ x = \dfrac { 3 - 5 } { 4 } \end{array}$
$\begin{array} {l} x = 2 \\ x = \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } } { 4 } \end{array}$
$ $ Subtract $ 5 $ from $ 3$
$\begin{array} {l} x = 2 \\ x = \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 2 } } { 4 } \end{array}$
$\begin{array} {l} x = 2 \\ x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 2 } } { \color{#FF6800}{ 4 } } } \end{array}$
$ $ Do the reduction of the fraction format $ $
$\begin{array} {l} x = 2 \\ x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \end{array}$
$\begin{array} {l} x = 2 \\ x = \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } { 2 } \end{array}$
$ $ Move the minus sign to the front of the fraction $ $
$\begin{array} {l} x = 2 \\ x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 2 } } } \end{array}$