Solve sqrt{2xy}dy/12=1

$$\sqrt { 2 x y } \frac { d y } { 12 } = 1$$

Solve for d (complex solution)

$$d=\frac{6\sqrt{2}\left(xy\right)^{-\frac{1}{2}}}{y}$$

$$y\neq 0\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12.

$$\sqrt{2xy}dy=12$$

Reorder the terms.

$$dy\sqrt{2xy}=12$$

The equation is in standard form.

$$y\sqrt{2xy}d=12$$

Divide both sides by y\sqrt{2xy}.

$$\frac{y\sqrt{2xy}d}{y\sqrt{2xy}}=\frac{12}{y\sqrt{2xy}}$$

Dividing by y\sqrt{2xy} undoes the multiplication by y\sqrt{2xy}.

$$d=\frac{12}{y\sqrt{2xy}}$$

Divide 12 by y\sqrt{2xy}.

$$d=\frac{12\times \left(2xy\right)^{-\frac{1}{2}}}{y}$$

Solve for d

$$d=\frac{6\sqrt{\frac{2}{xy}}}{y}$$

$$\left(x<0\text{ and }y<0\right)\text{ or }\left(y>0\text{ and }x>0\right)$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12.

$$\sqrt{2xy}dy=12$$

Reorder the terms.

$$dy\sqrt{2xy}=12$$

The equation is in standard form.

$$y\sqrt{2xy}d=12$$

Divide both sides by y\sqrt{2xy}.

$$\frac{y\sqrt{2xy}d}{y\sqrt{2xy}}=\frac{12}{y\sqrt{2xy}}$$

Dividing by y\sqrt{2xy} undoes the multiplication by y\sqrt{2xy}.

$$d=\frac{12}{y\sqrt{2xy}}$$

Solve for x

$$x=\frac{72}{d^{2}y^{3}}$$

$$\left(d<0\text{ and }y<0\right)\text{ or }\left(d>0\text{ and }y>0\right)$$

Steps for Solving Radical Equations

Divide both sides by \frac{1}{12}dy.

$$\frac{12\times \frac{dy}{12}\sqrt{2yx}}{dy}=\frac{12}{dy}$$

Dividing by \frac{1}{12}dy undoes the multiplication by \frac{1}{12}dy.

$$\sqrt{2yx}=\frac{12}{dy}$$

Square both sides of the equation.

$$2yx=\frac{144}{\left(dy\right)^{2}}$$

Divide both sides by 2y.

$$\frac{2yx}{2y}=\frac{144}{\left(dy\right)^{2}\times 2y}$$

Dividing by 2y undoes the multiplication by 2y.

$$x=\frac{144}{\left(dy\right)^{2}\times 2y}$$

Divide \frac{144}{\left(dy\right)^{2}} by 2y.

$$x=\frac{72}{d^{2}y^{3}}$$

Solve for x (complex solution)

$$x=\frac{72}{d^{2}y^{3}}$$

$$arg(\sqrt{\frac{1}{\left(dy\right)^{2}}}dy)<\pi \text{ and }y\neq 0\text{ and }d\neq 0$$