Solve x^3+ax+b=0

$$x ^ { 3 } + a x + b = 0$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Subtract x^{3} from both sides. Anything subtracted from zero gives its negation.

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

Subtract b from both sides.

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

The equation is in standard form.

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

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide -x^{3}-b by x.

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

Solve for a

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

Steps for Solving Linear Equation

Subtract x^{3} from both sides. Anything subtracted from zero gives its negation.

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

Subtract b from both sides.

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

The equation is in standard form.

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

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide -x^{3}-b by x.

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

Solve for b

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

Solution Steps

Subtract x^{3} from both sides. Anything subtracted from zero gives its negation.

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

Subtract ax from both sides.

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