Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{bx^{2}+c-e}{x^{3}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&c=e\text{ and }x=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=-\frac{ax^{3}+c-e}{x^{2}}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&c=e\text{ and }x=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{bx^{2}+c-e}{x^{3}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&c=e\text{ and }x=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-\frac{ax^{3}+c-e}{x^{2}}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=e\text{ and }x=0\end{matrix}\right.
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ax^{3}+c=e-bx^{2}
Subtract bx^{2} from both sides.
ax^{3}=e-bx^{2}-c
Subtract c from both sides.
ax^{3}=-bx^{2}-c+e
Reorder the terms.
x^{3}a=e-c-bx^{2}
The equation is in standard form.
\frac{x^{3}a}{x^{3}}=\frac{e-c-bx^{2}}{x^{3}}
Divide both sides by x^{3}.
a=\frac{e-c-bx^{2}}{x^{3}}
Dividing by x^{3} undoes the multiplication by x^{3}.
bx^{2}+c=e-ax^{3}
Subtract ax^{3} from both sides.
bx^{2}=e-ax^{3}-c
Subtract c from both sides.
bx^{2}=-ax^{3}-c+e
Reorder the terms.
x^{2}b=e-c-ax^{3}
The equation is in standard form.
\frac{x^{2}b}{x^{2}}=\frac{e-c-ax^{3}}{x^{2}}
Divide both sides by x^{2}.
b=\frac{e-c-ax^{3}}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
ax^{3}+c=e-bx^{2}
Subtract bx^{2} from both sides.
ax^{3}=e-bx^{2}-c
Subtract c from both sides.
ax^{3}=-bx^{2}-c+e
Reorder the terms.
x^{3}a=e-c-bx^{2}
The equation is in standard form.
\frac{x^{3}a}{x^{3}}=\frac{e-c-bx^{2}}{x^{3}}
Divide both sides by x^{3}.
a=\frac{e-c-bx^{2}}{x^{3}}
Dividing by x^{3} undoes the multiplication by x^{3}.
bx^{2}+c=e-ax^{3}
Subtract ax^{3} from both sides.
bx^{2}=e-ax^{3}-c
Subtract c from both sides.
bx^{2}=-ax^{3}-c+e
Reorder the terms.
x^{2}b=e-c-ax^{3}
The equation is in standard form.
\frac{x^{2}b}{x^{2}}=\frac{e-c-ax^{3}}{x^{2}}
Divide both sides by x^{2}.
b=\frac{e-c-ax^{3}}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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Limits
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