Solve v^2=4+8x

$$v ^ { 2 } = 4 + 8 x$$

Solve for x

$$x=\frac{v^{2}-4}{8}$$

Steps for Solving Linear Equation

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

$$4+8x=v^{2}$$

Subtract 4 from both sides.

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

Divide both sides by 8.

$$\frac{8x}{8}=\frac{v^{2}-4}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{v^{2}-4}{8}$$

Divide v^{2}-4 by 8.

$$x=\frac{v^{2}}{8}-\frac{1}{2}$$

Solve for v (complex solution)

$$v=-2\sqrt{2x+1}$$

$$v=2\sqrt{2x+1}$$

Solve for v

$$v=2\sqrt{2x+1}$$

$$v=-2\sqrt{2x+1}\text{, }x\geq -\frac{1}{2}$$