# Calculator search results

Formula
Solve an expression involving the absolute value
Graph
$y = x ^ { 2 } - | x | - 20$
$y = 0$
$x ^{ 2 } - | x | -20 = 0$
$\begin{array} {l} x = - 5 \\ x = 5 \end{array}$
 Solve a solution to $x$
$x ^ { 2 } - | x | \color{#FF6800}{ - } \color{#FF6800}{ 20 } = 0$
 Move the constant to the right side and change the sign 
$x ^ { 2 } - | x | = \color{#FF6800}{ 20 }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } | \color{#FF6800}{ x } | = \color{#FF6800}{ 20 }$
 Divide the interval based on the value where the inside of the absolute value is 0 
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) = \color{#FF6800}{ 20 } \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 0 } \right ) \\ \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } = \color{#FF6800}{ 20 } \left ( \text{However (or only)} \color{#FF6800}{ x } \geq \color{#FF6800}{ 0 } \right )$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) = \color{#FF6800}{ 20 } \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 0 } \right ) \\ \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ x } = \color{#FF6800}{ 20 } \left ( \text{However (or only)} \color{#FF6800}{ x } \geq \color{#FF6800}{ 0 } \right )$
 Find the solution 
$\left. \begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ 4 } \end{array} \right\} \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 0 } \right ) \\ \left. \begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 4 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ 5 } \end{array} \right\} \left ($ However (or only) $\color{#FF6800}{ x } \geq \color{#FF6800}{ 0 } \right )$
$\left. \begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ 4 } \end{array} \right\} \left ( \text{However (or only)} \color{#FF6800}{ x } < \color{#FF6800}{ 0 } \right ) \\ \left. \begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 4 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ 5 } \end{array} \right\} \left ($ However (or only) $\color{#FF6800}{ x } \geq \color{#FF6800}{ 0 } \right )$
 Make sure if the value is within the interval 
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ 5 }$
$\color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ 5 }$
 Find the union of sets of each interval 
$\begin{array} {l} \color{#FF6800}{ x } = \color{#FF6800}{ - } \color{#FF6800}{ 5 } \\ \color{#FF6800}{ x } = \color{#FF6800}{ 5 } \end{array}$
 그래프 보기 
Graph
Solution search results
Economics & Finance
Have you found the solution you wanted?
Try again
Try more features at QANDA!
Search by problem image
Ask 1:1 question to TOP class teachers
AI recommend problems and video lecture