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Formula
Solve the quadratic equation
Answer
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$$x ^ { 2 } - 5 x - 6 = 3$$
$\begin{array} {l} x = \dfrac { 5 + \sqrt{ 61 } } { 2 } \\ x = \dfrac { 5 - \sqrt{ 61 } } { 2 } \end{array}$
Calculate using the quadratic formula
$x ^ { 2 } - 5 x - 6 = \color{#FF6800}{ 3 }$
$ $ Move the expression to the left side and change the symbol $ $
$x ^ { 2 } - 5 x - 6 \color{#FF6800}{ - } \color{#FF6800}{ 3 } = 0$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 6 } \color{#FF6800}{ - } \color{#FF6800}{ 3 } = \color{#FF6800}{ 0 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 \pm \sqrt{ \left ( - 5 \right ) ^ { 2 } - 4 \times 1 \times \left ( - 9 \right ) } } { 2 \times 1 } }$
$x = \dfrac { 5 \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right ) ^ { \color{#FF6800}{ 2 } } - 4 \times 1 \times \left ( - 9 \right ) } } { 2 \times 1 }$
$ $ Remove negative signs because negative numbers raised to even powers are positive $ $
$x = \dfrac { 5 \pm \sqrt{ 5 ^ { 2 } - 4 \times 1 \times \left ( - 9 \right ) } } { 2 \times 1 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 \pm \sqrt{ 5 ^ { 2 } - 4 \times 1 \times \left ( - 9 \right ) } } { 2 \times 1 } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 \pm \sqrt{ 61 } } { 2 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 \pm \sqrt{ 61 } } { 2 } }$
$ $ Separate the answer $ $
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 + \sqrt{ 61 } } { 2 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 5 - \sqrt{ 61 } } { 2 } } \end{array}$
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