$\left ( \color{#FF6800}{ 40 } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) \left ( \color{#FF6800}{ 20 } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) = 576$
$ $ Expand using $ \left(a + b\right)\left(c + d\right) = ac + ad + bc + bd$
$\color{#FF6800}{ 40 } \color{#FF6800}{ \times } \color{#FF6800}{ 20 } \color{#FF6800}{ + } \color{#FF6800}{ 40 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ \times } \color{#FF6800}{ 20 } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) = 576$
$\color{#FF6800}{ 40 } \color{#FF6800}{ \times } \color{#FF6800}{ 20 } \color{#FF6800}{ + } \color{#FF6800}{ 40 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ \times } \color{#FF6800}{ 20 } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) = \color{#FF6800}{ 576 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ 800 } \color{#FF6800}{ - } \color{#FF6800}{ 40 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 20 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ x } \color{#FF6800}{ x } = \color{#FF6800}{ 576 }$
$800 - 40 x - 20 x + \color{#FF6800}{ x } x = 576$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$800 - 40 x - 20 x + \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } } x = 576$
$800 - 40 x - 20 x + x ^ { 1 } \color{#FF6800}{ x } = 576$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$800 - 40 x - 20 x + x ^ { 1 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } } = 576$
$800 - 40 x - 20 x + \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } } = 576$
$ $ Add the exponent as the base is the same $ $
$800 - 40 x - 20 x + \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } = 576$
$\color{#FF6800}{ 800 } \color{#FF6800}{ - } \color{#FF6800}{ 40 } \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 20 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } = \color{#FF6800}{ 576 }$
$ $ Organize the expression $ $
$\color{#FF6800}{ 800 } \color{#FF6800}{ - } \color{#FF6800}{ 60 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } = \color{#FF6800}{ 576 }$
$800 - 60 x + x ^ { 2 } = \color{#FF6800}{ 576 }$
$ $ Move the expression to the left side and change the symbol $ $
$800 - 60 x + x ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 576 } = 0$
$\color{#FF6800}{ 800 } - 60 x + x ^ { 2 } \color{#FF6800}{ - } \color{#FF6800}{ 576 } = 0$
$ $ Subtract $ 576 $ from $ 800$
$\color{#FF6800}{ 224 } - 60 x + x ^ { 2 } = 0$
$\color{#FF6800}{ 224 } - 60 x \color{#FF6800}{ + } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } = 0$
$ $ Organize $ x $ in descending power $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } - 60 x \color{#FF6800}{ + } \color{#FF6800}{ 224 } = 0$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 60 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 224 } = \color{#FF6800}{ 0 }$
$ $ Solve the quadratic equation $ ax^{2}+bx+c=0 $ using the quadratic formula $ \dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 60 } \right ) \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 60 } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 224 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } }$
$x = \dfrac { \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 60 \right ) \pm \sqrt{ \left ( - 60 \right ) ^ { 2 } - 4 \times 1 \times 224 } } { 2 \times 1 }$
$ $ Simplify Minus $ $
$x = \dfrac { 60 \pm \sqrt{ \left ( - 60 \right ) ^ { 2 } - 4 \times 1 \times 224 } } { 2 \times 1 }$
$x = \dfrac { 60 \pm \sqrt{ \left ( \color{#FF6800}{ - } \color{#FF6800}{ 60 } \right ) ^ { \color{#FF6800}{ 2 } } - 4 \times 1 \times 224 } } { 2 \times 1 }$
$ $ Remove negative signs because negative numbers raised to even powers are positive $ $
$x = \dfrac { 60 \pm \sqrt{ 60 ^ { 2 } - 4 \times 1 \times 224 } } { 2 \times 1 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 60 } \pm \sqrt{ \color{#FF6800}{ 60 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \color{#FF6800}{ \times } \color{#FF6800}{ 224 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } }$
$ $ Organize the expression $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 60 } \pm \sqrt{ \color{#FF6800}{ 2704 } } } { \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 1 } } }$
$x = \dfrac { 60 \pm \sqrt{ \color{#FF6800}{ 2704 } } } { 2 \times 1 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$x = \dfrac { 60 \pm \color{#FF6800}{ 52 } } { 2 \times 1 }$
$x = \dfrac { 60 \pm 52 } { 2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } }$
$ $ Multiplying any number by 1 does not change the value $ $
$x = \dfrac { 60 \pm 52 } { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 60 } \pm \color{#FF6800}{ 52 } } { \color{#FF6800}{ 2 } } }$
$ $ Separate the answer $ $
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 60 } \color{#FF6800}{ + } \color{#FF6800}{ 52 } } { \color{#FF6800}{ 2 } } } \\ \color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 60 } \color{#FF6800}{ - } \color{#FF6800}{ 52 } } { \color{#FF6800}{ 2 } } } \end{array}$
$\begin{array} {l} x = \dfrac { \color{#FF6800}{ 60 } \color{#FF6800}{ + } \color{#FF6800}{ 52 } } { 2 } \\ x = \dfrac { 60 - 52 } { 2 } \end{array}$
$ $ Add $ 60 $ and $ 52$
$\begin{array} {l} x = \dfrac { \color{#FF6800}{ 112 } } { 2 } \\ x = \dfrac { 60 - 52 } { 2 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 112 } } { \color{#FF6800}{ 2 } } } \\ x = \dfrac { 60 - 52 } { 2 } \end{array}$
$ $ Do the reduction of the fraction format $ $
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 56 } } { \color{#FF6800}{ 1 } } } \\ x = \dfrac { 60 - 52 } { 2 } \end{array}$
$\begin{array} {l} x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 56 } } { \color{#FF6800}{ 1 } } } \\ x = \dfrac { 60 - 52 } { 2 } \end{array}$
$ $ Reduce the fraction to the lowest term $ $
$\begin{array} {l} x = \color{#FF6800}{ 56 } \\ x = \dfrac { 60 - 52 } { 2 } \end{array}$
$\begin{array} {l} x = 56 \\ x = \dfrac { \color{#FF6800}{ 60 } \color{#FF6800}{ - } \color{#FF6800}{ 52 } } { 2 } \end{array}$
$ $ Subtract $ 52 $ from $ 60$
$\begin{array} {l} x = 56 \\ x = \dfrac { \color{#FF6800}{ 8 } } { 2 } \end{array}$
$\begin{array} {l} x = 56 \\ x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 8 } } { \color{#FF6800}{ 2 } } } \end{array}$
$ $ Do the reduction of the fraction format $ $
$\begin{array} {l} x = 56 \\ x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } } { \color{#FF6800}{ 1 } } } \end{array}$
$\begin{array} {l} x = 56 \\ x = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 4 } } { \color{#FF6800}{ 1 } } } \end{array}$
$ $ Reduce the fraction to the lowest term $ $
$\begin{array} {l} x = 56 \\ x = \color{#FF6800}{ 4 } \end{array}$