Solve m=sqrt{n+2x}

$$m = \sqrt { n + 2 x }$$

Solve for n

$$n=m^{2}-2x$$

$$m\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{n+2x}=m$$

Square both sides of the equation.

$$n+2x=m^{2}$$

Subtract 2x from both sides of the equation.

$$n+2x-2x=m^{2}-2x$$

Subtracting 2x from itself leaves 0.

$$n=m^{2}-2x$$

Solve for m (complex solution)

$$m=\sqrt{2x+n}$$

Solve for n (complex solution)

$$n=m^{2}-2x$$

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

Solve for m

$$m=\sqrt{2x+n}$$

$$n\geq -2x$$