Solve for I (complex solution)
\left\{\begin{matrix}I=-\frac{Jx+K}{x^{2}}\text{, }&x\neq 0\\I\in \mathrm{C}\text{, }&K=0\text{ and }x=0\end{matrix}\right.
Solve for J (complex solution)
\left\{\begin{matrix}J=-Ix-\frac{K}{x}\text{, }&x\neq 0\\J\in \mathrm{C}\text{, }&K=0\text{ and }x=0\end{matrix}\right.
Solve for I
\left\{\begin{matrix}I=-\frac{Jx+K}{x^{2}}\text{, }&x\neq 0\\I\in \mathrm{R}\text{, }&K=0\text{ and }x=0\end{matrix}\right.
Solve for J
\left\{\begin{matrix}J=-Ix-\frac{K}{x}\text{, }&x\neq 0\\J\in \mathrm{R}\text{, }&K=0\text{ and }x=0\end{matrix}\right.
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Ix^{2}+K=-Jx
Subtract Jx from both sides. Anything subtracted from zero gives its negation.
Ix^{2}=-Jx-K
Subtract K from both sides.
x^{2}I=-Jx-K
The equation is in standard form.
\frac{x^{2}I}{x^{2}}=\frac{-Jx-K}{x^{2}}
Divide both sides by x^{2}.
I=\frac{-Jx-K}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
I=-\frac{Jx+K}{x^{2}}
Divide -Jx-K by x^{2}.
Jx+K=-Ix^{2}
Subtract Ix^{2} from both sides. Anything subtracted from zero gives its negation.
Jx=-Ix^{2}-K
Subtract K from both sides.
xJ=-Ix^{2}-K
The equation is in standard form.
\frac{xJ}{x}=\frac{-Ix^{2}-K}{x}
Divide both sides by x.
J=\frac{-Ix^{2}-K}{x}
Dividing by x undoes the multiplication by x.
J=-Ix-\frac{K}{x}
Divide -Ix^{2}-K by x.
Ix^{2}+K=-Jx
Subtract Jx from both sides. Anything subtracted from zero gives its negation.
Ix^{2}=-Jx-K
Subtract K from both sides.
x^{2}I=-Jx-K
The equation is in standard form.
\frac{x^{2}I}{x^{2}}=\frac{-Jx-K}{x^{2}}
Divide both sides by x^{2}.
I=\frac{-Jx-K}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
I=-\frac{Jx+K}{x^{2}}
Divide -Jx-K by x^{2}.
Jx+K=-Ix^{2}
Subtract Ix^{2} from both sides. Anything subtracted from zero gives its negation.
Jx=-Ix^{2}-K
Subtract K from both sides.
xJ=-Ix^{2}-K
The equation is in standard form.
\frac{xJ}{x}=\frac{-Ix^{2}-K}{x}
Divide both sides by x.
J=\frac{-Ix^{2}-K}{x}
Dividing by x undoes the multiplication by x.
J=-Ix-\frac{K}{x}
Divide -Ix^{2}-K by x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}