Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{bx+c+11}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&c=-11\text{ and }x=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=-\frac{ax^{2}+c+11}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&c=-11\text{ and }x=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{bx+c+11}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&c=-11\text{ and }x=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-\frac{ax^{2}+c+11}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=-11\text{ and }x=0\end{matrix}\right.
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ax^{2}+bx+c=-11
Subtract 11 from 0 to get -11.
ax^{2}+c=-11-bx
Subtract bx from both sides.
ax^{2}=-11-bx-c
Subtract c from both sides.
x^{2}a=-bx-c-11
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{-bx-c-11}{x^{2}}
Divide both sides by x^{2}.
a=\frac{-bx-c-11}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
a=-\frac{bx+c+11}{x^{2}}
Divide -11-bx-c by x^{2}.
ax^{2}+bx+c=-11
Subtract 11 from 0 to get -11.
bx+c=-11-ax^{2}
Subtract ax^{2} from both sides.
bx=-11-ax^{2}-c
Subtract c from both sides.
bx=-ax^{2}-c-11
Reorder the terms.
xb=-ax^{2}-c-11
The equation is in standard form.
\frac{xb}{x}=\frac{-ax^{2}-c-11}{x}
Divide both sides by x.
b=\frac{-ax^{2}-c-11}{x}
Dividing by x undoes the multiplication by x.
b=-\frac{ax^{2}+c+11}{x}
Divide -ax^{2}-c-11 by x.
ax^{2}+bx+c=-11
Subtract 11 from 0 to get -11.
ax^{2}+c=-11-bx
Subtract bx from both sides.
ax^{2}=-11-bx-c
Subtract c from both sides.
x^{2}a=-bx-c-11
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{-bx-c-11}{x^{2}}
Divide both sides by x^{2}.
a=\frac{-bx-c-11}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
a=-\frac{bx+c+11}{x^{2}}
Divide -11-bx-c by x^{2}.
ax^{2}+bx+c=-11
Subtract 11 from 0 to get -11.
bx+c=-11-ax^{2}
Subtract ax^{2} from both sides.
bx=-11-ax^{2}-c
Subtract c from both sides.
bx=-ax^{2}-c-11
Reorder the terms.
xb=-ax^{2}-c-11
The equation is in standard form.
\frac{xb}{x}=\frac{-ax^{2}-c-11}{x}
Divide both sides by x.
b=\frac{-ax^{2}-c-11}{x}
Dividing by x undoes the multiplication by x.
b=-\frac{ax^{2}+c+11}{x}
Divide -ax^{2}-c-11 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
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