Solve x^3+ax=b

$${ x }^{ 3 } +ax = b$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{b-x^{3}}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{3} from both sides.

$$ax=b-x^{3}$$

The equation is in standard form.

$$xa=b-x^{3}$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{b-x^{3}}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{b-x^{3}}{x}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{b-x^{3}}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{3} from both sides.

$$ax=b-x^{3}$$

The equation is in standard form.

$$xa=b-x^{3}$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{b-x^{3}}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{b-x^{3}}{x}$$

Solve for b

$$b=x\left(x^{2}+a\right)$$

Solution Steps

Swap sides so that all variable terms are on the left hand side.

$$b=x^{3}+ax$$