Solve ysqrt{2x}=12

$$y \sqrt{ 2x } =12$$

Solve for y (complex solution)

$$y=6\sqrt{2}x^{-\frac{1}{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\sqrt{2x}y=12$$

Divide both sides by \sqrt{2x}.

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

Dividing by \sqrt{2x} undoes the multiplication by \sqrt{2x}.

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

Divide 12 by \sqrt{2x}.

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

Solve for x

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

$$y>0$$

Steps for Solving Radical Equations

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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

Square both sides of the equation.

$$2x=\frac{144}{y^{2}}$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{144}{2y^{2}}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{144}{2y^{2}}$$

Divide \frac{144}{y^{2}} by 2.

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

Solve for y

$$y=6\sqrt{\frac{2}{x}}$$

$$x>0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\sqrt{2x}y=12$$

Divide both sides by \sqrt{2x}.

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

Dividing by \sqrt{2x} undoes the multiplication by \sqrt{2x}.

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

Solve for x (complex solution)

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

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