Solve sqrt{2x}-sqrt{3y}=-1

$$\sqrt{ 2x } - \sqrt{ 3y } =-1$$

Solve for x

$$x=\frac{\left(-\sqrt{3y}+1\right)^{2}}{2}$$

$$y\geq \frac{1}{3}$$

Steps for Solving Radical Equations

Subtract -\sqrt{3y} from both sides of the equation.

$$\sqrt{2x}-\sqrt{3y}-\left(-\sqrt{3y}\right)=-1-\left(-\sqrt{3y}\right)$$

Subtracting -\sqrt{3y} from itself leaves 0.

$$\sqrt{2x}=-1-\left(-\sqrt{3y}\right)$$

Subtract -\sqrt{3y} from -1.

$$\sqrt{2x}=\sqrt{3y}-1$$

Square both sides of the equation.

$$2x=\left(\sqrt{3y}-1\right)^{2}$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{\left(\sqrt{3y}-1\right)^{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{\left(\sqrt{3y}-1\right)^{2}}{2}$$

Solve for y

$$y=\frac{\left(\sqrt{2x}+1\right)^{2}}{3}$$

$$x\geq 0$$

Steps for Solving Radical Equations

Subtract \sqrt{2x} from both sides of the equation.

$$-\sqrt{3y}+\sqrt{2x}-\sqrt{2x}=-1-\sqrt{2x}$$

Subtracting \sqrt{2x} from itself leaves 0.

$$-\sqrt{3y}=-1-\sqrt{2x}$$

Subtract \sqrt{2x} from -1.

$$-\sqrt{3y}=-\sqrt{2x}-1$$

Divide both sides by -1.

$$\frac{-\sqrt{3y}}{-1}=\frac{-\sqrt{2x}-1}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{3y}=\frac{-\sqrt{2x}-1}{-1}$$

Divide -1-\sqrt{2x} by -1.

$$\sqrt{3y}=\sqrt{2x}+1$$

Square both sides of the equation.

$$3y=\left(\sqrt{2x}+1\right)^{2}$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{\left(\sqrt{2x}+1\right)^{2}}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{\left(\sqrt{2x}+1\right)^{2}}{3}$$

Solve for x (complex solution)

$$x=\frac{\left(-\sqrt{3y}+1\right)^{2}}{2}$$

$$y=\frac{1}{3}\text{ or }arg(-\sqrt{3y}+1)\geq \pi$$

Solve for y (complex solution)

$$y=\frac{\left(\sqrt{2x}+1\right)^{2}}{3}$$

$$arg(\sqrt{2x}+1)<\pi$$