Solve for x
\left\{\begin{matrix}x=3\text{, }&|y|\leq 9\\x\in \begin{bmatrix}-\sqrt{\left(-|y|+9\right)\left(|y|+1\right)}+3,\sqrt{\left(-|y|+9\right)\left(|y|+1\right)}+3\end{bmatrix}\text{, }&|y|<9\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y\in \begin{bmatrix}-\left(\sqrt{-\left(x-8\right)\left(x+2\right)}+4\right),\sqrt{-\left(x-8\right)\left(x+2\right)}+4\end{bmatrix}\text{, }&x\geq 0\text{ and }x\leq 6\\y\in \begin{bmatrix}-\left(\sqrt{-\left(x-8\right)\left(x+2\right)}+4\right),\sqrt{\left(-x-2\right)\left(x-8\right)}-4\end{bmatrix}\cup \begin{bmatrix}-\sqrt{-\left(x-8\right)\left(x+2\right)}+4,\sqrt{-\left(x-8\right)\left(x+2\right)}+4\end{bmatrix}\text{, }&\left(x>-2\text{ and }x<0\right)\text{ or }\left(x>6\text{ and }x<8\right)\\y=-4\text{; }y=4\text{, }&x\geq -2\text{ and }x\leq 8\end{matrix}\right.
Graph
Share
Copied to clipboard
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}