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Formula
Factorize by the perfect square formula
$$x ^ { 2 } + x + \dfrac { 1 } { 4 }$$
$\dfrac { 1 } { 4 } \left ( 2 x + 1 \right ) ^ { 2 }$
Express as the perfect square formula
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 4 } } }$
 Bind the expressions with the common factor $\dfrac { 1 } { 4 }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 4 } } } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right )$
$\dfrac { 1 } { 4 } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + 4 x + 1 \right )$
 Present as the shape of the power 
$\dfrac { 1 } { 4 } \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + 4 x + 1 \right )$
$\dfrac { 1 } { 4 } \left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } + 4 x + 1 \right )$
 Binding the power 
$\dfrac { 1 } { 4 } \left ( \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ 2 } } + 4 x + 1 \right )$
$\dfrac { 1 } { 4 } \left ( \left ( 2 x \right ) ^ { 2 } + 4 x + \color{#FF6800}{ 1 } \right )$
 Present as the shape of the power 
$\dfrac { 1 } { 4 } \left ( \left ( 2 x \right ) ^ { 2 } + 4 x + \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right )$
$\dfrac { 1 } { 4 } \left ( \left ( 2 x \right ) ^ { 2 } + \color{#FF6800}{ 4 } \color{#FF6800}{ x } + 1 ^ { 2 } \right )$
 Change the term in the middle 
$\dfrac { 1 } { 4 } \left ( \left ( 2 x \right ) ^ { 2 } + \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 1 } + 1 ^ { 2 } \right )$
$\dfrac { 1 } { 4 } \left ( \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \right )$
 Organize the expression using $A^{2} ± 2AB + B^2 = (A ± B)^{2}$
$\dfrac { 1 } { 4 } \left ( \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) ^ { \color{#FF6800}{ 2 } }$
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