Solve y=sqrt{1/4x+2}

$$y = \sqrt{ \frac{ 1 }{ 4 } x+2 }$$

Solve for x

$$x=4\left(y^{2}-2\right)$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{\frac{1}{4}x+2}=y$$

Square both sides of the equation.

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

Subtract 2 from both sides of the equation.

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

Subtracting 2 from itself leaves 0.

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

Multiply both sides by 4.

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

Dividing by \frac{1}{4} undoes the multiplication by \frac{1}{4}.

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

Divide y^{2}-2 by \frac{1}{4} by multiplying y^{2}-2 by the reciprocal of \frac{1}{4}.

$$x=4y^{2}-8$$

Solve for x (complex solution)

$$x=4\left(y^{2}-2\right)$$

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

Solve for y (complex solution)

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

Solve for y

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

$$x\geq -8$$