Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{bx^{2}+x_{0}-y}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&y=x_{0}\text{ and }x=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=-\frac{ax+x_{0}-y}{x^{2}}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&y=x_{0}\text{ and }x=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{bx^{2}+x_{0}-y}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=x_{0}\text{ and }x=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-\frac{ax+x_{0}-y}{x^{2}}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&y=x_{0}\text{ and }x=0\end{matrix}\right.
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x_{0}+ax+bx^{2}=y
Swap sides so that all variable terms are on the left hand side.
ax+bx^{2}=y-x_{0}
Subtract x_{0} from both sides.
ax=y-x_{0}-bx^{2}
Subtract bx^{2} from both sides.
ax=-bx^{2}-x_{0}+y
Reorder the terms.
xa=y-x_{0}-bx^{2}
The equation is in standard form.
\frac{xa}{x}=\frac{y-x_{0}-bx^{2}}{x}
Divide both sides by x.
a=\frac{y-x_{0}-bx^{2}}{x}
Dividing by x undoes the multiplication by x.
x_{0}+ax+bx^{2}=y
Swap sides so that all variable terms are on the left hand side.
ax+bx^{2}=y-x_{0}
Subtract x_{0} from both sides.
bx^{2}=y-x_{0}-ax
Subtract ax from both sides.
x^{2}b=y-x_{0}-ax
The equation is in standard form.
\frac{x^{2}b}{x^{2}}=\frac{y-x_{0}-ax}{x^{2}}
Divide both sides by x^{2}.
b=\frac{y-x_{0}-ax}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
x_{0}+ax+bx^{2}=y
Swap sides so that all variable terms are on the left hand side.
ax+bx^{2}=y-x_{0}
Subtract x_{0} from both sides.
ax=y-x_{0}-bx^{2}
Subtract bx^{2} from both sides.
ax=-bx^{2}-x_{0}+y
Reorder the terms.
xa=y-x_{0}-bx^{2}
The equation is in standard form.
\frac{xa}{x}=\frac{y-x_{0}-bx^{2}}{x}
Divide both sides by x.
a=\frac{y-x_{0}-bx^{2}}{x}
Dividing by x undoes the multiplication by x.
x_{0}+ax+bx^{2}=y
Swap sides so that all variable terms are on the left hand side.
ax+bx^{2}=y-x_{0}
Subtract x_{0} from both sides.
bx^{2}=y-x_{0}-ax
Subtract ax from both sides.
x^{2}b=y-x_{0}-ax
The equation is in standard form.
\frac{x^{2}b}{x^{2}}=\frac{y-x_{0}-ax}{x^{2}}
Divide both sides by x^{2}.
b=\frac{y-x_{0}-ax}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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Limits
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