$\color{#FF6800}{ x } \left ( \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 15 } \right ) = 5 \left ( x - 5 \right )$
$ $ 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 $ $
$x ^ { 2 } + \color{#FF6800}{ 10 } \color{#FF6800}{ x } + 25 = 0$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 10 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 25 } = \color{#FF6800}{ 0 }$
$ $ Determine the number of roots using discriminant, $ D=b^{2}-4ac $ from quadratic equation, $ ax^{2}+bx+c=0$
$\color{#FF6800}{ D } = \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 25 }$
$D = \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 2 } } - 4 \times 1 \times 25$
$ $ Calculate power $ $
$D = \color{#FF6800}{ 100 } - 4 \times 1 \times 25$
$D = 100 - 4 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \times 25$
$ $ Multiplying any number by 1 does not change the value $ $
$D = 100 - 4 \times 25$
$D = 100 \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 25 }$
$ $ Multiply $ - 4 $ and $ 25$
$D = 100 \color{#FF6800}{ - } \color{#FF6800}{ 100 }$
$D = \color{#FF6800}{ 100 } \color{#FF6800}{ - } \color{#FF6800}{ 100 }$
$ $ Remove the two numbers if the values are the same and the signs are different $ $
$D = 0$
$\color{#FF6800}{ D } = \color{#FF6800}{ 0 }$
$ $ Since $ D=0 $ , the number of real root of the following quadratic equation is 1 (multiple root) $ $
$ $ 1 real root (multiple root) $ $