Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{y^{2}}{4x_{5}}\text{, }&x_{5}\neq 0\\x\in \mathrm{C}\text{, }&y=0\text{ and }x_{5}=0\end{matrix}\right.
Solve for x_5 (complex solution)
\left\{\begin{matrix}x_{5}=\frac{y^{2}}{4x}\text{, }&x\neq 0\\x_{5}\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{y^{2}}{4x_{5}}\text{, }&x_{5}\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }x_{5}=0\end{matrix}\right.
Solve for x_5
\left\{\begin{matrix}x_{5}=\frac{y^{2}}{4x}\text{, }&x\neq 0\\x_{5}\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.
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4x_{5}x=y^{2}
Swap sides so that all variable terms are on the left hand side.
\frac{4x_{5}x}{4x_{5}}=\frac{y^{2}}{4x_{5}}
Divide both sides by 4x_{5}.
x=\frac{y^{2}}{4x_{5}}
Dividing by 4x_{5} undoes the multiplication by 4x_{5}.
4x_{5}x=y^{2}
Swap sides so that all variable terms are on the left hand side.
4xx_{5}=y^{2}
The equation is in standard form.
\frac{4xx_{5}}{4x}=\frac{y^{2}}{4x}
Divide both sides by 4x.
x_{5}=\frac{y^{2}}{4x}
Dividing by 4x undoes the multiplication by 4x.
4x_{5}x=y^{2}
Swap sides so that all variable terms are on the left hand side.
\frac{4x_{5}x}{4x_{5}}=\frac{y^{2}}{4x_{5}}
Divide both sides by 4x_{5}.
x=\frac{y^{2}}{4x_{5}}
Dividing by 4x_{5} undoes the multiplication by 4x_{5}.
4x_{5}x=y^{2}
Swap sides so that all variable terms are on the left hand side.
4xx_{5}=y^{2}
The equation is in standard form.
\frac{4xx_{5}}{4x}=\frac{y^{2}}{4x}
Divide both sides by 4x.
x_{5}=\frac{y^{2}}{4x}
Dividing by 4x undoes the multiplication by 4x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
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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}