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Formula
Solve the quadratic equation
Answer
$$x ^ { 2 } - 4 x - 5 = 0$$
$\begin{array} {l} x = 5 \\ x = - 1 \end{array}$
Solve quadratic equations using the square root
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } = \color{#FF6800}{ 0 }$
 Convert the quadratic expression on the left side to a perfect square format 
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ 0 }$
$\left ( x - 2 \right ) ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } = 0$
 Move the constant to the right side and change the sign 
$\left ( x - 2 \right ) ^ { 2 } = \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } }$
$\left ( x - 2 \right ) ^ { 2 } = 5 + \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } }$
 Calculate power 
$\left ( x - 2 \right ) ^ { 2 } = 5 + \color{#FF6800}{ 4 }$
$\left ( x - 2 \right ) ^ { 2 } = \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 4 }$
 Add $5$ and $4$
$\left ( x - 2 \right ) ^ { 2 } = \color{#FF6800}{ 9 }$
$\left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ 9 }$
 Solve quadratic equations using the square root 
$\color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } = \pm \sqrt{ \color{#FF6800}{ 9 } }$
$\color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 2 } = \pm \sqrt{ \color{#FF6800}{ 9 } }$
 Solve a solution to $x$
$\color{#FF6800}{ x } = \pm \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
$\color{#FF6800}{ x } = \pm \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
 Separate the answer 
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \\ x = 2 - 3 \end{array}$
 Add $2$ and $3$
$\begin{array} {l} x = \color{#FF6800}{ 5 } \\ x = 2 - 3 \end{array}$
$\begin{array} {l} x = 5 \\ x = \color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } \end{array}$
 Subtract $3$ from $2$
$\begin{array} {l} x = 5 \\ x = \color{#FF6800}{ - } \color{#FF6800}{ 1 } \end{array}$
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