Solve ax^2-x=0

$$a x ^ { 2 } - x = 0$$

Solve for a

$$\left\{\begin{matrix}a=\frac{1}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add x to both sides. Anything plus zero gives itself.

$$ax^{2}=x$$

The equation is in standard form.

$$x^{2}a=x$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{x}{x^{2}}$$

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

$$a=\frac{x}{x^{2}}$$

Divide x by x^{2}.

$$a=\frac{1}{x}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\frac{1}{a}\text{, }&a\neq 0\end{matrix}\right.$$