Solve 5m+sqrt{2z}=6

$$5 m + \sqrt { 2 z } = 6$$

Solve for m (complex solution)

$$m=\frac{-\sqrt{2z}+6}{5}$$

Steps for Solving Linear Equation

Subtract \sqrt{2z} from both sides.

$$5m=6-\sqrt{2z}$$

The equation is in standard form.

$$5m=-\sqrt{2z}+6$$

Divide both sides by 5.

$$\frac{5m}{5}=\frac{-\sqrt{2z}+6}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$m=\frac{-\sqrt{2z}+6}{5}$$

Solve for m

$$m=\frac{-\sqrt{2z}+6}{5}$$

$$z\geq 0$$

Steps for Solving Linear Equation

Subtract \sqrt{2z} from both sides.

$$5m=6-\sqrt{2z}$$

The equation is in standard form.

$$5m=-\sqrt{2z}+6$$

Divide both sides by 5.

$$\frac{5m}{5}=\frac{-\sqrt{2z}+6}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$m=\frac{-\sqrt{2z}+6}{5}$$

Solve for z

$$z=\frac{\left(6-5m\right)^{2}}{2}$$

$$6-5m\geq 0$$

Steps for Solving Radical Equations

Subtract 5m from both sides of the equation.

$$\sqrt{2z}+5m-5m=6-5m$$

Subtracting 5m from itself leaves 0.

$$\sqrt{2z}=6-5m$$

Square both sides of the equation.

$$2z=\left(6-5m\right)^{2}$$

Divide both sides by 2.

$$\frac{2z}{2}=\frac{\left(6-5m\right)^{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$z=\frac{\left(6-5m\right)^{2}}{2}$$

Solve for z (complex solution)

$$z=\frac{\left(6-5m\right)^{2}}{2}$$

$$m=\frac{6}{5}\text{ or }arg(6-5m)<\pi$$