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Formula
Solve the quadratic equation
Answer
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$$x ^ { 2 } + x + 1 = 0$$
$\begin{array} {l} x = \dfrac { - 1 + \sqrt{ 3 } i } { 2 } \\ x = \dfrac { - 1 - \sqrt{ 3 } i } { 2 } \end{array}$
Calculate using the quodratic formula$($Imaginary root solution$)
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } = \color{#FF6800}{ 0 }$
$ $ Solve the quadratic equation $ ax^{2}+bx+c=0 $ using the quadratic formula $ \dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 1 \pm \sqrt{ 1 ^ { 2 } - 4 \times 1 \times 1 } } { 2 \times 1 } }$
$x = \dfrac { - 1 \pm \sqrt{ \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } - 4 \times 1 \times 1 } } { 2 \times 1 }$
$ $ Calculate power $ $
$x = \dfrac { - 1 \pm \sqrt{ \color{#FF6800}{ 1 } - 4 \times 1 \times 1 } } { 2 \times 1 }$
$x = \dfrac { - 1 \pm \sqrt{ 1 - 4 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } } { 2 \times 1 }$
$ $ Multiplying any number by 1 does not change the value $ $
$x = \dfrac { - 1 \pm \sqrt{ 1 - 4 } } { 2 \times 1 }$
$x = \dfrac { - 1 \pm \sqrt{ \color{#FF6800}{ 1 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } } } { 2 \times 1 }$
$ $ Subtract $ 4 $ from $ 1$
$x = \dfrac { - 1 \pm \sqrt{ \color{#FF6800}{ - } \color{#FF6800}{ 3 } } } { 2 \times 1 }$
$x = \dfrac { - 1 \pm \sqrt{ - 3 } } { 2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
$ $ Multiplying any number by 1 does not change the value $ $
$x = \dfrac { - 1 \pm \sqrt{ - 3 } } { \color{#FF6800}{ 2 } }$
$x = \dfrac { - 1 \pm \sqrt{ \color{#FF6800}{ - } 3 } } { 2 }$
$ $ Subtracting (-) from the square root gives i $ $
$x = \dfrac { - 1 \pm \sqrt{ 3 } \color{#FF6800}{ i } } { 2 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 1 \pm \sqrt{ 3 } i } { 2 } }$
$ $ Separate the answer $ $
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 1 + \sqrt{ 3 } i } { 2 } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 1 - \sqrt{ 3 } i } { 2 } } \end{array}$
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