Solve for J (complex solution)
\left\{\begin{matrix}\\J=\frac{x-1}{2}\text{, }&\text{unconditionally}\\J\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for J
\left\{\begin{matrix}\\J=\frac{x-1}{2}\text{, }&\text{unconditionally}\\J\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x
x=2J+1
x=0
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\frac{1}{2}x^{2}-\frac{1}{2}x=xJ
Use the distributive property to multiply \frac{1}{2}x by x-1.
xJ=\frac{1}{2}x^{2}-\frac{1}{2}x
Swap sides so that all variable terms are on the left hand side.
xJ=\frac{x^{2}-x}{2}
The equation is in standard form.
\frac{xJ}{x}=\frac{x\left(x-1\right)}{2x}
Divide both sides by x.
J=\frac{x\left(x-1\right)}{2x}
Dividing by x undoes the multiplication by x.
J=\frac{x-1}{2}
Divide \frac{x\left(-1+x\right)}{2} by x.
\frac{1}{2}x^{2}-\frac{1}{2}x=xJ
Use the distributive property to multiply \frac{1}{2}x by x-1.
xJ=\frac{1}{2}x^{2}-\frac{1}{2}x
Swap sides so that all variable terms are on the left hand side.
xJ=\frac{x^{2}-x}{2}
The equation is in standard form.
\frac{xJ}{x}=\frac{x\left(x-1\right)}{2x}
Divide both sides by x.
J=\frac{x\left(x-1\right)}{2x}
Dividing by x undoes the multiplication by x.
J=\frac{x-1}{2}
Divide \frac{x\left(-1+x\right)}{2} by x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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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}