Solve y=sqrt{k+5m}

$$y = \sqrt { k + 5 m }$$

Solve for k

$$k=y^{2}-5m$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{k+5m}=y$$

Square both sides of the equation.

$$k+5m=y^{2}$$

Subtract 5m from both sides of the equation.

$$k+5m-5m=y^{2}-5m$$

Subtracting 5m from itself leaves 0.

$$k=y^{2}-5m$$

Solve for m

$$m=\frac{y^{2}-k}{5}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{k+5m}=y$$

Square both sides of the equation.

$$5m+k=y^{2}$$

Subtract k from both sides of the equation.

$$5m+k-k=y^{2}-k$$

Subtracting k from itself leaves 0.

$$5m=y^{2}-k$$

Divide both sides by 5.

$$\frac{5m}{5}=\frac{y^{2}-k}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$m=\frac{y^{2}-k}{5}$$

Solve for k (complex solution)

$$k=y^{2}-5m$$

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

Solve for m (complex solution)

$$m=\frac{y^{2}-k}{5}$$

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