$\color{#FF6800}{ x } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 15 } \right ) = 5 \left ( x - 5 \right )$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 15 } \color{#FF6800}{ x } = 5 \left ( x - 5 \right )$
$x ^ { 2 } + 15 x = \color{#FF6800}{ 5 } \left ( \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \right )$
$ $ Organize the expression $ $
$x ^ { 2 } + 15 x = \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 25 }$
$x ^ { 2 } + 15 x = \color{#FF6800}{ 5 } \color{#FF6800}{ x } - 25$
$ $ Move the expression to the left side and change the symbol $ $
$x ^ { 2 } + 15 x \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 25 } = 0$
$x ^ { 2 } + \color{#FF6800}{ 15 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 5 } \color{#FF6800}{ x } + 25 = 0$
$ $ Calculate between similar terms $ $
$x ^ { 2 } + \color{#FF6800}{ 10 } \color{#FF6800}{ x } + 25 = 0$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 25 } = \color{#FF6800}{ 0 }$
$ $ Solve the quadratic equation $ ax^{2}+bx+c=0 $ using the quadratic formula $ \dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 10 } \pm \sqrt{ \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 25 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 10 } \pm \sqrt{ \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 25 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 10 } \pm \sqrt{ \color{#FF6800}{ 0 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } }$
$x = \dfrac { - 10 \pm \sqrt{ \color{#FF6800}{ 0 } } } { 2 \times 1 }$
$n square root $ of 0 is 0 $ $
$x = \dfrac { - 10 \pm \color{#FF6800}{ 0 } } { 2 \times 1 }$
$x = \dfrac { - 10 \pm 0 } { 2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
$ $ Multiplying any number by 1 does not change the value $ $
$x = \dfrac { - 10 \pm 0 } { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 10 } \pm \color{#FF6800}{ 0 } } { \color{#FF6800}{ 2 } } }$
$ $ The value will not be changed even if adding or subtracting 0 $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { \color{#FF6800}{ 2 } } }$
$x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { \color{#FF6800}{ 2 } } }$
$ $ Do the reduction of the fraction format $ $
$x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \color{#FF6800}{ 5 } } { \color{#FF6800}{ 1 } } }$
$x = \dfrac { - 5 } { \color{#FF6800}{ 1 } }$
$ $ If the denominator is 1, the denominator can be removed $ $
$x = \color{#FF6800}{ - } \color{#FF6800}{ 5 }$