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Formula
Solve the quadratic equation
Answer
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$$x ^ { 2 } = 5$$
$\begin{array} {l} x = \sqrt{ 5 } \\ x = - \sqrt{ 5 } \end{array}$
Calculate using the quadratic formula
$x ^ { 2 } = \color{#FF6800}{ 5 }$
$ $ Move the expression to the left side and change the symbol $ $
$x ^ { 2 } - 5 = 0$
$x = \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 0 } \pm \sqrt{ 0 ^ { 2 } - 4 \times 1 \times \left ( - 5 \right ) } } { 2 \times 1 }$
$ $ 0 has no sign $ $
$x = \dfrac { \color{#FF6800}{ 0 } \pm \sqrt{ 0 ^ { 2 } - 4 \times 1 \times \left ( - 5 \right ) } } { 2 \times 1 }$
$x = \dfrac { 0 \pm \sqrt{ \color{#FF6800}{ 0 } ^ { \color{#FF6800}{ 2 } } - 4 \times 1 \times \left ( - 5 \right ) } } { 2 \times 1 }$
$ $ The power of 0 is 0 $ $
$x = \dfrac { 0 \pm \sqrt{ \color{#FF6800}{ 0 } - 4 \times 1 \times \left ( - 5 \right ) } } { 2 \times 1 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 0 \pm \sqrt{ 0 - 4 \times 1 \times \left ( - 5 \right ) } } { 2 \times 1 } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 0 \pm \sqrt{ 20 } } { 2 \times 1 } }$
$x = \dfrac { 0 \pm \sqrt{ \color{#FF6800}{ 20 } } } { 2 \times 1 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$x = \dfrac { 0 \pm \color{#FF6800}{ 2 } \sqrt{ \color{#FF6800}{ 5 } } } { 2 \times 1 }$
$x = \dfrac { 0 \pm 2 \sqrt{ 5 } } { 2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
$ $ Multiplying any number by 1 does not change the value $ $
$x = \dfrac { 0 \pm 2 \sqrt{ 5 } } { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 0 \pm 2 \sqrt{ 5 } } { 2 } }$
$ $ Separate the answer $ $
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 0 + 2 \sqrt{ 5 } } { 2 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 0 - 2 \sqrt{ 5 } } { 2 } } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { 0 + 2 \sqrt{ 5 } } { 2 } } \\ x = \dfrac { 0 - 2 \sqrt{ 5 } } { 2 } \end{array}$
$ $ Simplify the fraction $ $
$\begin{array} {l} x = \color{#FF6800}{ 0 } \color{#FF6800}{ + } \sqrt{ \color{#FF6800}{ 5 } } \\ x = \dfrac { 0 - 2 \sqrt{ 5 } } { 2 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ 0 } + \sqrt{ 5 } \\ x = \dfrac { 0 - 2 \sqrt{ 5 } } { 2 } \end{array}$
$ $ 0 does not change when you add or subtract $ $
$\begin{array} {l} x = \sqrt{ 5 } \\ x = \dfrac { 0 - 2 \sqrt{ 5 } } { 2 } \end{array}$
$\begin{array} {l} x = \sqrt{ 5 } \\ x = \color{#FF6800}{ \dfrac { 0 - 2 \sqrt{ 5 } } { 2 } } \end{array}$
$ $ Simplify the fraction $ $
$\begin{array} {l} x = \sqrt{ 5 } \\ x = \color{#FF6800}{ 0 } \color{#FF6800}{ - } \sqrt{ \color{#FF6800}{ 5 } } \end{array}$
$\begin{array} {l} x = \sqrt{ 5 } \\ x = \color{#FF6800}{ 0 } - \sqrt{ 5 } \end{array}$
$ $ 0 does not change when you add or subtract $ $
$\begin{array} {l} x = \sqrt{ 5 } \\ x = - \sqrt{ 5 } \end{array}$
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