Solve for a (complex solution)
\left\{\begin{matrix}a=-x-\frac{b}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=0\text{ and }x=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-x-\frac{b}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=0\text{ and }x=0\end{matrix}\right.
Solve for b
b=-x\left(x+a\right)
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ax+b=-x^{2}
Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.
ax=-x^{2}-b
Subtract b from both sides.
xa=-x^{2}-b
The equation is in standard form.
\frac{xa}{x}=\frac{-x^{2}-b}{x}
Divide both sides by x.
a=\frac{-x^{2}-b}{x}
Dividing by x undoes the multiplication by x.
a=-x-\frac{b}{x}
Divide -x^{2}-b by x.
ax+b=-x^{2}
Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.
ax=-x^{2}-b
Subtract b from both sides.
xa=-x^{2}-b
The equation is in standard form.
\frac{xa}{x}=\frac{-x^{2}-b}{x}
Divide both sides by x.
a=\frac{-x^{2}-b}{x}
Dividing by x undoes the multiplication by x.
a=-x-\frac{b}{x}
Divide -x^{2}-b by x.
ax+b=-x^{2}
Subtract x^{2} from both sides. Anything subtracted from zero gives its negation.
b=-x^{2}-ax
Subtract ax from both sides.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}