Solve V=sqrt{4x-2}

$$V = \sqrt { 4 x - 2 }$$

Solve for x

$$x=\frac{V^{2}+2}{4}$$

$$V\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{4x-2}=V$$

Square both sides of the equation.

$$4x-2=V^{2}$$

Add 2 to both sides of the equation.

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

Subtracting -2 from itself leaves 0.

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

Subtract -2 from V^{2}.

$$4x=V^{2}+2$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{V^{2}+2}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{V^{2}+2}{4}$$

Divide V^{2}+2 by 4.

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

Solve for x (complex solution)

$$x=\frac{V^{2}+2}{4}$$

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

Solve for V

$$V=\sqrt{4x-2}$$

$$x\geq \frac{1}{2}$$