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Formula
Solve the quadratic equation
Answer
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$$x ^ { 2 } - 5 x + 1 = 0$$
$\begin{array} {l} x = \dfrac { 5 + \sqrt{ 21 } } { 2 } \\ x = \dfrac { 5 - \sqrt{ 21 } } { 2 } \end{array}$
Calculate using the quadratic formula
$x = \dfrac { \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 5 \right ) \pm \sqrt{ \left ( - 5 \right ) ^ { 2 } - 4 \times 1 \times 1 } } { 2 \times 1 }$
$ $ Simplify Minus $ $
$x = \dfrac { 5 \pm \sqrt{ \left ( - 5 \right ) ^ { 2 } - 4 \times 1 \times 1 } } { 2 \times 1 }$
$x = \dfrac { 5 \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) ^ { \color{#FF6800}{ 2 } } - 4 \times 1 \times 1 } } { 2 \times 1 }$
$ $ Remove negative signs because negative numbers raised to even powers are positive $ $
$x = \dfrac { 5 \pm \sqrt{ 5 ^ { 2 } - 4 \times 1 \times 1 } } { 2 \times 1 }$
$x = \dfrac { 5 \pm \sqrt{ \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } - 4 \times 1 \times 1 } } { 2 \times 1 }$
$ $ Calculate power $ $
$x = \dfrac { 5 \pm \sqrt{ \color{#FF6800}{ 25 } - 4 \times 1 \times 1 } } { 2 \times 1 }$
$x = \dfrac { 5 \pm \sqrt{ 25 - 4 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } } { 2 \times 1 }$
$ $ Multiplying any number by 1 does not change the value $ $
$x = \dfrac { 5 \pm \sqrt{ 25 - 4 } } { 2 \times 1 }$
$x = \dfrac { 5 \pm \sqrt{ \color{#FF6800}{ 25 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } } } { 2 \times 1 }$
$ $ Subtract $ 4 $ from $ 25$
$x = \dfrac { 5 \pm \sqrt{ \color{#FF6800}{ 21 } } } { 2 \times 1 }$
$x = \dfrac { 5 \pm \sqrt{ 21 } } { 2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
$ $ Multiplying any number by 1 does not change the value $ $
$x = \dfrac { 5 \pm \sqrt{ 21 } } { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 \pm \sqrt{ 21 } } { 2 } }$
$ $ Separate the answer $ $
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 + \sqrt{ 21 } } { 2 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 - \sqrt{ 21 } } { 2 } } \end{array}$
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