Solve 2(qx^2-1)=x

$$2 ( q x ^ { 2 } - 1 ) = x$$

Solve for q

$$q=\frac{x+2}{2x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by qx^{2}-1.

$$2qx^{2}-2=x$$

Add 2 to both sides.

$$2qx^{2}=x+2$$

The equation is in standard form.

$$2x^{2}q=x+2$$

Divide both sides by 2x^{2}.

$$\frac{2x^{2}q}{2x^{2}}=\frac{x+2}{2x^{2}}$$

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

$$q=\frac{x+2}{2x^{2}}$$

Divide x+2 by 2x^{2}.

$$q=\frac{1}{2x}+\frac{1}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{16q+1}+1}{4q}\text{; }x=\frac{-\sqrt{16q+1}+1}{4q}\text{, }&q\neq 0\\x=-2\text{, }&q=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{16q+1}+1}{4q}\text{; }x=\frac{-\sqrt{16q+1}+1}{4q}\text{, }&q\neq 0\text{ and }q\geq -\frac{1}{16}\\x=-2\text{, }&q=0\end{matrix}\right.$$