Solve ab^2+c=x

$$a b ^ { 2 } + c = x$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{c-x}{b^{2}}\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&c=x\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract c from both sides.

$$ab^{2}=x-c$$

The equation is in standard form.

$$b^{2}a=x-c$$

Divide both sides by b^{2}.

$$\frac{b^{2}a}{b^{2}}=\frac{x-c}{b^{2}}$$

Dividing by b^{2} undoes the multiplication by b^{2}.

$$a=\frac{x-c}{b^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{c-x}{b^{2}}\text{, }&b\neq 0\\a\in \mathrm{R}\text{, }&c=x\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract c from both sides.

$$ab^{2}=x-c$$

The equation is in standard form.

$$b^{2}a=x-c$$

Divide both sides by b^{2}.

$$\frac{b^{2}a}{b^{2}}=\frac{x-c}{b^{2}}$$

Dividing by b^{2} undoes the multiplication by b^{2}.

$$a=\frac{x-c}{b^{2}}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-ia^{-\frac{1}{2}}\sqrt{c-x}\text{; }b=ia^{-\frac{1}{2}}\sqrt{c-x}\text{, }&a\neq 0\\b\in \mathrm{C}\text{, }&c=x\text{ and }a=0\end{matrix}\right.$$

Solve for b

$$\left\{\begin{matrix}b=\sqrt{\frac{x-c}{a}}\text{; }b=-\sqrt{\frac{x-c}{a}}\text{, }&\left(a>0\text{ or }c\geq x\right)\text{ and }\left(a<0\text{ or }c\leq x\right)\text{ and }a\neq 0\\b\in \mathrm{R}\text{, }&c=x\text{ and }a=0\end{matrix}\right.$$