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

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

Solve for x

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

$$y\geq 0$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

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

Multiply both sides by 2.

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

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

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

Divide y by \frac{1}{2} by multiplying y by the reciprocal of \frac{1}{2}.

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

Square both sides of the equation.

$$2x=4y^{2}$$

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide 4y^{2} by 2.

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

Solve for x (complex solution)

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

$$arg(y)<\pi \text{ or }y=0$$

Solve for y

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

$$x\geq 0$$