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Formula
Solve the quadratic equation
$$x ^ { 2 } - 3 x = 0$$
$\begin{array} {l} x = 3 \\ x = 0 \end{array}$
Calculate using the quadratic formula
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } = 0$
 Bind the expressions with the common factor $x$
$\color{#FF6800}{ x } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) = 0$
$x = \dfrac { \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 3 \right ) \pm \sqrt{ \left ( - 3 \right ) ^ { 2 } - 4 \times 1 \times 0 } } { 2 \times 1 }$
 Simplify Minus 
$x = \dfrac { 3 \pm \sqrt{ \left ( - 3 \right ) ^ { 2 } - 4 \times 1 \times 0 } } { 2 \times 1 }$
$x = \dfrac { 3 \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \right ) ^ { \color{#FF6800}{ 2 } } - 4 \times 1 \times 0 } } { 2 \times 1 }$
 Remove negative signs because negative numbers raised to even powers are positive 
$x = \dfrac { 3 \pm \sqrt{ 3 ^ { 2 } - 4 \times 1 \times 0 } } { 2 \times 1 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 \pm \sqrt{ 3 ^ { 2 } - 4 \times 1 \times 0 } } { 2 \times 1 } }$
 Organize the expression 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 \pm \sqrt{ 9 } } { 2 \times 1 } }$
$x = \dfrac { 3 \pm \sqrt{ \color{#FF6800}{ 9 } } } { 2 \times 1 }$
 Organize the part that can be taken out of the radical sign inside the square root symbol 
$x = \dfrac { 3 \pm \color{#FF6800}{ 3 } } { 2 \times 1 }$
$x = \dfrac { 3 \pm 3 } { 2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
 Multiplying any number by 1 does not change the value 
$x = \dfrac { 3 \pm 3 } { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 \pm 3 } { 2 } }$
 Separate the answer 
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 + 3 } { 2 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 - 3 } { 2 } } \end{array}$
$\begin{array} {l} x = \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } } { 2 } \\ x = \dfrac { 3 - 3 } { 2 } \end{array}$
 Add $3$ and $3$
$\begin{array} {l} x = \dfrac { \color{#FF6800}{ 6 } } { 2 } \\ x = \dfrac { 3 - 3 } { 2 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { 6 } { 2 } } \\ x = \dfrac { 3 - 3 } { 2 } \end{array}$
 Do the reduction of the fraction format 
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { 3 } { 1 } } \\ x = \dfrac { 3 - 3 } { 2 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { 3 } { 1 } } \\ x = \dfrac { 3 - 3 } { 2 } \end{array}$
 Reduce the fraction to the lowest term 
$\begin{array} {l} x = \color{#FF6800}{ 3 } \\ x = \dfrac { 3 - 3 } { 2 } \end{array}$
$\begin{array} {l} x = 3 \\ x = \dfrac { \color{#FF6800}{ 3 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } } { 2 } \end{array}$
 Remove the two numbers if the values are the same and the signs are different 
$\begin{array} {l} x = 3 \\ x = \dfrac { 0 } { 2 } \end{array}$
$\begin{array} {l} x = 3 \\ x = \color{#FF6800}{ \dfrac { 0 } { 2 } } \end{array}$
 If the numerator is 0, it is equal to 0 
$\begin{array} {l} x = 3 \\ x = \color{#FF6800}{ 0 } \end{array}$
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