Solve for f (complex solution)
\left\{\begin{matrix}\\f=\sqrt{m\left(m-2x\right)}\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=\sqrt{m\left(m-2x\right)}\text{, }&\left(m\geq 2x\text{ or }m\leq 0\text{ or }x\leq 0\right)\text{ and }\left(x\geq 0\text{ or }m\geq 0\text{ or }m\leq 2x\right)\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for m (complex solution)
\left\{\begin{matrix}m=\sqrt{x^{2}+f^{2}}+x\text{; }m=-\sqrt{x^{2}+f^{2}}+x\text{, }&arg(f)<\pi \text{ or }f=0\\m\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for m
\left\{\begin{matrix}m=\sqrt{x^{2}+f^{2}}+x\text{; }m=-\sqrt{x^{2}+f^{2}}+x\text{, }&f\geq 0\\m=2x\text{, }&f=0\\m=0\text{, }&x\geq 0\text{ and }f=0\\m\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
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Linear Equation
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\frac{ \sqrt{ { m }^{ 2 } -2mx } x }{ \frac{ 2 }{ 2 } } = fx
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\frac{\sqrt{m^{2}-2mx}x}{1}=fx
Divide 2 by 2 to get 1.
\sqrt{m^{2}-2mx}x=fx
Anything divided by one gives itself.
fx=\sqrt{m^{2}-2mx}x
Swap sides so that all variable terms are on the left hand side.
xf=x\sqrt{m^{2}-2mx}
The equation is in standard form.
\frac{xf}{x}=\frac{x\sqrt{m\left(m-2x\right)}}{x}
Divide both sides by x.
f=\frac{x\sqrt{m\left(m-2x\right)}}{x}
Dividing by x undoes the multiplication by x.
f=\sqrt{m\left(m-2x\right)}
Divide \sqrt{m\left(m-2x\right)}x by x.
\frac{\sqrt{m^{2}-2mx}x}{1}=fx
Divide 2 by 2 to get 1.
\sqrt{m^{2}-2mx}x=fx
Anything divided by one gives itself.
fx=\sqrt{m^{2}-2mx}x
Swap sides so that all variable terms are on the left hand side.
xf=x\sqrt{m^{2}-2mx}
The equation is in standard form.
\frac{xf}{x}=\frac{x\sqrt{m\left(m-2x\right)}}{x}
Divide both sides by x.
f=\frac{x\sqrt{m\left(m-2x\right)}}{x}
Dividing by x undoes the multiplication by x.
f=\sqrt{m\left(m-2x\right)}
Divide \sqrt{m\left(m-2x\right)}x by x.
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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 ) }
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\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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