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Formula
Solve the equation
Graph
$y = \sqrt{ 3 } x + x$
$y = 10$
$x$-intercept
$\left ( 0 , 0 \right )$
$y$-intercept
$\left ( 0 , 0 \right )$
$\sqrt{ 3 } x+x = 10$
$x = 5 \sqrt{ 3 } - 5$
 Solve a solution to $x$
$\sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ x } = 10$
 Organize the expression 
$\left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ x } = 10$
$\left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \color{#FF6800}{ x } = \color{#FF6800}{ 10 }$
 Divide both sides by the same number 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 10 } { \sqrt{ 3 } + 1 } }$
$x = \dfrac { 10 } { \sqrt{ 3 } + 1 }$
 Find the conjugate irrational number of denominator 
$x = \color{#FF6800}{ \dfrac { 10 } { \sqrt{ 3 } + 1 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \sqrt{ 3 } - 1 } { \sqrt{ 3 } - 1 } }$
$x = \dfrac { 10 } { \sqrt{ 3 } + 1 } \times \dfrac { \sqrt{ 3 } - 1 } { \sqrt{ 3 } - 1 }$
 The denominator is multiplied by denominator, and the numerator is multiplied by numerator 
$x = \color{#FF6800}{ \dfrac { 10 \left ( \sqrt{ 3 } - 1 \right ) } { \left ( \sqrt{ 3 } + 1 \right ) \left ( \sqrt{ 3 } - 1 \right ) } }$
$x = \dfrac { \color{#FF6800}{ 10 } \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) } { \left ( \sqrt{ 3 } + 1 \right ) \left ( \sqrt{ 3 } - 1 \right ) }$
 Multiply each term in parentheses by $10$
$x = \dfrac { \color{#FF6800}{ 10 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 10 } } { \left ( \sqrt{ 3 } + 1 \right ) \left ( \sqrt{ 3 } - 1 \right ) }$
$x = \dfrac { 10 \sqrt{ 3 } - 10 } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) \left ( \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } \right ) }$
 Expand the expression using $\left(a - b\right)\left(a + b\right) = a^{2} - b^{2}$
$x = \dfrac { 10 \sqrt{ 3 } - 10 } { \left ( \sqrt{ \color{#FF6800}{ 3 } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } }$
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 10 \sqrt{ 3 } - 10 } { \left ( \sqrt{ 3 } \right ) ^ { 2 } - 1 ^ { 2 } } }$
 Organize the expression 
$\color{#FF6800}{ x } = \color{#FF6800}{ \dfrac { 10 \sqrt{ 3 } - 10 } { 2 } }$
$x = \color{#FF6800}{ \dfrac { 10 \sqrt{ 3 } - 10 } { 2 } }$
 Reduce the fraction 
$x = \color{#FF6800}{ 5 } \sqrt{ \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 5 }$
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