Solve for f (complex solution)
\left\{\begin{matrix}\\f=0\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&f_{C}=x^{3}\end{matrix}\right.
Solve for f_C (complex solution)
\left\{\begin{matrix}\\f_{C}=x^{3}\text{, }&\text{unconditionally}\\f_{C}\in \mathrm{C}\text{, }&f=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}\\f=0\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&f_{C}=x^{3}\end{matrix}\right.
Solve for f_C
\left\{\begin{matrix}\\f_{C}=x^{3}\text{, }&\text{unconditionally}\\f_{C}\in \mathrm{R}\text{, }&f=0\end{matrix}\right.
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f_{C}f=x^{3}f
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
f_{C}f-x^{3}f=0
Subtract x^{3}f from both sides.
-fx^{3}+ff_{C}=0
Reorder the terms.
\left(-x^{3}+f_{C}\right)f=0
Combine all terms containing f.
\left(f_{C}-x^{3}\right)f=0
The equation is in standard form.
f=0
Divide 0 by f_{C}-x^{3}.
f_{C}f=x^{3}f
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
ff_{C}=fx^{3}
The equation is in standard form.
\frac{ff_{C}}{f}=\frac{fx^{3}}{f}
Divide both sides by f.
f_{C}=\frac{fx^{3}}{f}
Dividing by f undoes the multiplication by f.
f_{C}=x^{3}
Divide x^{3}f by f.
f_{C}f=x^{3}f
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
f_{C}f-x^{3}f=0
Subtract x^{3}f from both sides.
-fx^{3}+ff_{C}=0
Reorder the terms.
\left(-x^{3}+f_{C}\right)f=0
Combine all terms containing f.
\left(f_{C}-x^{3}\right)f=0
The equation is in standard form.
f=0
Divide 0 by f_{C}-x^{3}.
f_{C}f=x^{3}f
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
ff_{C}=fx^{3}
The equation is in standard form.
\frac{ff_{C}}{f}=\frac{fx^{3}}{f}
Divide both sides by f.
f_{C}=\frac{fx^{3}}{f}
Dividing by f undoes the multiplication by f.
f_{C}=x^{3}
Divide x^{3}f by f.
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}