f ( x ) = 2 \sqrt { 2 - 3 x } d x
Solve for d (complex solution)
\left\{\begin{matrix}d=\frac{\left(2-3x\right)^{-\frac{1}{2}}f}{2}\text{, }&x\neq \frac{2}{3}\\d\in \mathrm{C}\text{, }&x=0\text{ or }\left(f=0\text{ and }x=\frac{2}{3}\right)\end{matrix}\right.
Solve for f (complex solution)
\left\{\begin{matrix}\\f=2\sqrt{2-3x}d\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for d
\left\{\begin{matrix}d=\frac{f}{2\sqrt{2-3x}}\text{, }&x<\frac{2}{3}\\d\in \mathrm{R}\text{, }&x=0\text{ or }\left(f=0\text{ and }x=\frac{2}{3}\right)\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=2\sqrt{2-3x}d\text{, }&x\leq \frac{2}{3}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
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2\sqrt{2-3x}dx=fx
Swap sides so that all variable terms are on the left hand side.
2\sqrt{2-3x}xd=fx
The equation is in standard form.
\frac{2\sqrt{2-3x}xd}{2\sqrt{2-3x}x}=\frac{fx}{2\sqrt{2-3x}x}
Divide both sides by 2\sqrt{2-3x}x.
d=\frac{fx}{2\sqrt{2-3x}x}
Dividing by 2\sqrt{2-3x}x undoes the multiplication by 2\sqrt{2-3x}x.
d=\frac{\left(2-3x\right)^{-\frac{1}{2}}f}{2}
Divide fx by 2\sqrt{2-3x}x.
xf=2\sqrt{2-3x}dx
The equation is in standard form.
\frac{xf}{x}=\frac{2\sqrt{2-3x}dx}{x}
Divide both sides by x.
f=\frac{2\sqrt{2-3x}dx}{x}
Dividing by x undoes the multiplication by x.
f=2\sqrt{2-3x}d
Divide 2\sqrt{2-3x}dx by x.
2\sqrt{2-3x}dx=fx
Swap sides so that all variable terms are on the left hand side.
2\sqrt{2-3x}xd=fx
The equation is in standard form.
\frac{2\sqrt{2-3x}xd}{2\sqrt{2-3x}x}=\frac{fx}{2\sqrt{2-3x}x}
Divide both sides by 2\sqrt{2-3x}x.
d=\frac{fx}{2\sqrt{2-3x}x}
Dividing by 2\sqrt{2-3x}x undoes the multiplication by 2\sqrt{2-3x}x.
d=\frac{f}{2\sqrt{2-3x}}
Divide fx by 2\sqrt{2-3x}x.
xf=2\sqrt{2-3x}dx
The equation is in standard form.
\frac{xf}{x}=\frac{2\sqrt{2-3x}dx}{x}
Divide both sides by x.
f=\frac{2\sqrt{2-3x}dx}{x}
Dividing by x undoes the multiplication by x.
f=2\sqrt{2-3x}d
Divide 2\sqrt{2-3x}dx by x.
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