Solve xy-2y^2=1

$$x y - 2 y ^ { 2 } = 1$$

Solve for x

$$x=2y+\frac{1}{y}$$

$$y\neq 0$$

Steps for Solving Linear Equation

Add 2y^{2} to both sides.

$$xy=1+2y^{2}$$

The equation is in standard form.

$$yx=2y^{2}+1$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{2y^{2}+1}{y}$$

Dividing by y undoes the multiplication by y.

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

Divide 1+2y^{2} by y.

$$x=2y+\frac{1}{y}$$

Solve for y (complex solution)

$$y=\frac{-\sqrt{x^{2}-8}+x}{4}$$

$$y=\frac{\sqrt{x^{2}-8}+x}{4}$$

Solve for y

$$y=\frac{-\sqrt{x^{2}-8}+x}{4}$$

$$y=\frac{\sqrt{x^{2}-8}+x}{4}\text{, }|x|\geq 2\sqrt{2}$$