Solve xy=frac{sqrt{2}}{2x}

$$x y = \frac { \sqrt { 2 } } { 2 x }$$

Solve for y

$$y=\frac{\sqrt{2}}{2x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x.

$$xy\times 2x=\sqrt{2}$$

Multiply x and x to get x^{2}.

$$x^{2}y\times 2=\sqrt{2}$$

The equation is in standard form.

$$2x^{2}y=\sqrt{2}$$

Divide both sides by 2x^{2}.

$$\frac{2x^{2}y}{2x^{2}}=\frac{\sqrt{2}}{2x^{2}}$$

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

$$y=\frac{\sqrt{2}}{2x^{2}}$$

Solve for x (complex solution)

$$x=-\frac{2^{\frac{3}{4}}y^{-\frac{1}{2}}}{2}$$

$$x=\frac{2^{\frac{3}{4}}y^{-\frac{1}{2}}}{2}\text{, }y\neq 0$$

Solve for x

$$x=\frac{2^{\frac{3}{4}}}{2\sqrt{y}}$$

$$x=-\frac{2^{\frac{3}{4}}}{2\sqrt{y}}\text{, }y>0$$