Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{x^{2}+3x+y^{4}-2}{9x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&\left(y=\sqrt[4]{2}\text{ or }y=\sqrt[4]{2}i\text{ or }y=-\sqrt[4]{2}\text{ or }y=-\sqrt[4]{2}i\right)\text{ and }x=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{x^{2}+3x+y^{4}-2}{9x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }|y|=\sqrt[4]{2}\end{matrix}\right.
Solve for x (complex solution)
x=\frac{\sqrt{17-54a+81a^{2}-4y^{4}}+9a-3}{2}
x=\frac{-\sqrt{17-54a+81a^{2}-4y^{4}}+9a-3}{2}
Solve for x
x=\frac{\sqrt{17-54a+81a^{2}-4y^{4}}+9a-3}{2}
x=\frac{-\sqrt{17-54a+81a^{2}-4y^{4}}+9a-3}{2}\text{, }|y|\leq \frac{\sqrt{2}\sqrt[4]{81a^{2}-54a+17}}{2}
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9ax=x^{2}+y^{4}-2+3x
Swap sides so that all variable terms are on the left hand side.
9xa=x^{2}+3x+y^{4}-2
The equation is in standard form.
\frac{9xa}{9x}=\frac{x^{2}+3x+y^{4}-2}{9x}
Divide both sides by 9x.
a=\frac{x^{2}+3x+y^{4}-2}{9x}
Dividing by 9x undoes the multiplication by 9x.
9ax=x^{2}+y^{4}-2+3x
Swap sides so that all variable terms are on the left hand side.
9xa=x^{2}+3x+y^{4}-2
The equation is in standard form.
\frac{9xa}{9x}=\frac{x^{2}+3x+y^{4}-2}{9x}
Divide both sides by 9x.
a=\frac{x^{2}+3x+y^{4}-2}{9x}
Dividing by 9x undoes the multiplication by 9x.
Examples
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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
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