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Formula
Solve the quadratic equation
Answer
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$$4 x ^ { 2 } + 4 x + 1 = 0$$
$x = - \dfrac { 1 } { 2 }$
Calculate using the quadratic formula
$x = \dfrac { - 4 \pm \sqrt{ \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 2 } } - 4 \times 4 \times 1 } } { 2 \times 4 }$
$ $ Calculate power $ $
$x = \dfrac { - 4 \pm \sqrt{ \color{#FF6800}{ 16 } - 4 \times 4 \times 1 } } { 2 \times 4 }$
$x = \dfrac { - 4 \pm \sqrt{ 16 - 4 \times 4 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } } { 2 \times 4 }$
$ $ Multiplying any number by 1 does not change the value $ $
$x = \dfrac { - 4 \pm \sqrt{ 16 - 4 \times 4 } } { 2 \times 4 }$
$x = \dfrac { - 4 \pm \sqrt{ 16 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } } } { 2 \times 4 }$
$ $ Multiply $ - 4 $ and $ 4$
$x = \dfrac { - 4 \pm \sqrt{ 16 \color{#FF6800}{ - } \color{#FF6800}{ 16 } } } { 2 \times 4 }$
$x = \dfrac { - 4 \pm \sqrt{ \color{#FF6800}{ 16 } \color{#FF6800}{ - } \color{#FF6800}{ 16 } } } { 2 \times 4 }$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$x = \dfrac { - 4 \pm \sqrt{ 0 } } { 2 \times 4 }$
$x = \dfrac { - 4 \pm \sqrt{ \color{#FF6800}{ 0 } } } { 2 \times 4 }$
$n square root $ of 0 is 0 $ $
$x = \dfrac { - 4 \pm \color{#FF6800}{ 0 } } { 2 \times 4 }$
$x = \dfrac { - 4 \pm 0 } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 4 } }$
$ $ Multiply $ 2 $ and $ 4$
$x = \dfrac { - 4 \pm 0 } { \color{#FF6800}{ 8 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 4 \pm 0 } { 8 } }$
$ $ The value will not be changed even if adding or subtracting 0 $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { - 4 } { 8 } }$
$x = \color{#FF6800}{ \dfrac { - 4 } { 8 } }$
$ $ Do the reduction of the fraction format $ $
$x = \color{#FF6800}{ \dfrac { - 1 } { 2 } }$
$x = \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 1 } } { 2 }$
$ $ Move the minus sign to the front of the fraction $ $
$x = \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } }$
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