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Formula
$$2 x ^ { 2 } - 3 x + 1 = 0$$
$\begin{array} {l} x = 1 \\ x = \dfrac { 1 } { 2 } \end{array}$
Solve quadratic equations using the square root
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } = \color{#FF6800}{ 0 }$
 Divide both sides by the coefficient of the leading highest term 
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 2 } } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 2 } } = \color{#FF6800}{ 0 }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 2 } } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 2 } } = \color{#FF6800}{ 0 }$
 Convert the quadratic expression on the left side to a perfect square format 
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 4 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ \dfrac { 3 } { 4 } } \right ) ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ 0 }$
$\left ( x - \dfrac { 3 } { 4 } \right ) ^ { 2 } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ \dfrac { 3 } { 4 } } \right ) ^ { \color{#FF6800}{ 2 } } = 0$
 Move the constant to the right side and change the sign 
$\left ( x - \dfrac { 3 } { 4 } \right ) ^ { 2 } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ + } \left ( \color{#FF6800}{ \dfrac { 3 } { 4 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$\left ( x - \dfrac { 3 } { 4 } \right ) ^ { 2 } = - \dfrac { 1 } { 2 } + \left ( \color{#FF6800}{ \dfrac { 3 } { 4 } } \right ) ^ { \color{#FF6800}{ 2 } }$
 When raising a fraction to the power, raise the numerator and denominator each to the power 
$\left ( x - \dfrac { 3 } { 4 } \right ) ^ { 2 } = - \dfrac { 1 } { 2 } + \dfrac { \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 2 } } }$
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 4 } } \right ) ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 ^ { 2 } } { 4 ^ { 2 } } }$
 Organize the expression 
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 4 } } \right ) ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ \dfrac { 1 } { 16 } }$
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 4 } } \right ) ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ \dfrac { 1 } { 16 } }$
 Solve quadratic equations using the square root 
$\color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 4 } } = \pm \sqrt{ \color{#FF6800}{ \dfrac { 1 } { 16 } } }$
$\color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 } { 4 } } = \pm \sqrt{ \color{#FF6800}{ \dfrac { 1 } { 16 } } }$
 Solve a solution to $x$
$\color{#FF6800}{ x } = \pm \color{#FF6800}{ \dfrac { 1 } { 4 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 } { 4 } }$
$\color{#FF6800}{ x } = \pm \color{#FF6800}{ \dfrac { 1 } { 4 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 3 } { 4 } }$
 Separate the answer 
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 } { 4 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 4 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 } { 4 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 4 } } \end{array}$
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 } { 4 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { 1 } { 4 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 3 } { 4 } } \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 4 } } \end{array}$
 Organize the expression 
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ 1 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 1 } { 2 } } \end{array}$
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