Solve 1/3+3x+2y-sqrt{4z}+2^2=0

$$\frac{ 1 }{ 3 } +3x+2y- \sqrt{ 4z } + { 2 }^{ 2 } =0$$

Solve for x

$$x=-\frac{2y}{3}+\frac{2\sqrt{z}}{3}-\frac{13}{9}$$

$$z\geq 0$$

Steps for Solving Linear Equation

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{3}+3x+2y-\sqrt{4z}+4=0$$

Add \frac{1}{3} and 4 to get \frac{13}{3}.

$$\frac{13}{3}+3x+2y-\sqrt{4z}=0$$

Subtract \frac{13}{3} from both sides. Anything subtracted from zero gives its negation.

$$3x+2y-\sqrt{4z}=-\frac{13}{3}$$

Subtract 2y from both sides.

$$3x-\sqrt{4z}=-\frac{13}{3}-2y$$

Add \sqrt{4z} to both sides.

$$3x=-\frac{13}{3}-2y+\sqrt{4z}$$

The equation is in standard form.

$$3x=-2y+\sqrt{4z}-\frac{13}{3}$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{-2y+2\sqrt{z}-\frac{13}{3}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{-2y+2\sqrt{z}-\frac{13}{3}}{3}$$

Divide -\frac{13}{3}-2y+2\sqrt{z} by 3.

$$x=-\frac{2y}{3}+\frac{2\sqrt{z}}{3}-\frac{13}{9}$$

Solve for y

$$y=-\frac{3x}{2}+\sqrt{z}-\frac{13}{6}$$

$$z\geq 0$$

Steps for Solving Linear Equation

Calculate 2 to the power of 2 and get 4.

$$\frac{1}{3}+3x+2y-\sqrt{4z}+4=0$$

Add \frac{1}{3} and 4 to get \frac{13}{3}.

$$\frac{13}{3}+3x+2y-\sqrt{4z}=0$$

Subtract \frac{13}{3} from both sides. Anything subtracted from zero gives its negation.

$$3x+2y-\sqrt{4z}=-\frac{13}{3}$$

Subtract 3x from both sides.

$$2y-\sqrt{4z}=-\frac{13}{3}-3x$$

Add \sqrt{4z} to both sides.

$$2y=-\frac{13}{3}-3x+\sqrt{4z}$$

The equation is in standard form.

$$2y=-3x+\sqrt{4z}-\frac{13}{3}$$

Divide both sides by 2.

$$\frac{2y}{2}=\frac{-3x+2\sqrt{z}-\frac{13}{3}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$y=\frac{-3x+2\sqrt{z}-\frac{13}{3}}{2}$$

Divide -\frac{13}{3}-3x+2\sqrt{z} by 2.

$$y=-\frac{3x}{2}+\sqrt{z}-\frac{13}{6}$$