Solve A*x^5-x=x

$$A \cdot x ^ { 5 } - x = x$$

Solve for A (complex solution)

$$\left\{\begin{matrix}A=\frac{2}{x^{4}}\text{, }&x\neq 0\\A\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add x to both sides.

$$Ax^{5}=x+x$$

Combine x and x to get 2x.

$$Ax^{5}=2x$$

The equation is in standard form.

$$x^{5}A=2x$$

Divide both sides by x^{5}.

$$\frac{x^{5}A}{x^{5}}=\frac{2x}{x^{5}}$$

Dividing by x^{5} undoes the multiplication by x^{5}.

$$A=\frac{2x}{x^{5}}$$

Divide 2x by x^{5}.

$$A=\frac{2}{x^{4}}$$

Solve for A

$$\left\{\begin{matrix}A=\frac{2}{x^{4}}\text{, }&x\neq 0\\A\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add x to both sides.

$$Ax^{5}=x+x$$

Combine x and x to get 2x.

$$Ax^{5}=2x$$

The equation is in standard form.

$$x^{5}A=2x$$

Divide both sides by x^{5}.

$$\frac{x^{5}A}{x^{5}}=\frac{2x}{x^{5}}$$

Dividing by x^{5} undoes the multiplication by x^{5}.

$$A=\frac{2x}{x^{5}}$$

Divide 2x by x^{5}.

$$A=\frac{2}{x^{4}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\sqrt[4]{2}iA^{-\frac{1}{4}}\text{; }x=\sqrt[4]{2}A^{-\frac{1}{4}}\text{; }x=-\sqrt[4]{2}A^{-\frac{1}{4}}\text{; }x=-\sqrt[4]{2}iA^{-\frac{1}{4}}\text{, }&A\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\sqrt[4]{\frac{2}{A}}\text{; }x=-\sqrt[4]{\frac{2}{A}}\text{, }&A>0\end{matrix}\right.$$