Solve for k (complex solution)
\left\{\begin{matrix}k=-\frac{i\left(x-3\right)^{-\frac{1}{2}}\sqrt{2\left(x+3\right)}}{3}\text{; }k=\frac{i\left(x-3\right)^{-\frac{1}{2}}\sqrt{2\left(x+3\right)}}{3}\text{, }&x\neq 3\\k\in \mathrm{C}\text{, }&x=3\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=3\text{, }&\text{unconditionally}\\x=-\frac{3\left(2-9k^{2}\right)}{9k^{2}+2}\text{, }&k\neq -\frac{\sqrt{2}i}{3}\text{ and }k\neq \frac{\sqrt{2}i}{3}\end{matrix}\right.
Solve for k
\left\{\begin{matrix}k=\frac{\sqrt{-\frac{2\left(x+3\right)}{x-3}}}{3}\text{; }k=-\frac{\sqrt{-\frac{2\left(x+3\right)}{x-3}}}{3}\text{, }&x\geq -3\text{ and }x<3\\k\in \mathrm{R}\text{, }&x=3\end{matrix}\right.
Solve for x
x=-\frac{3\left(2-9k^{2}\right)}{9k^{2}+2}
x=3
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}