Solve 5sqrt{x}-sqrt{y}=4

$$5 \sqrt { x } - \sqrt { y } = 4$$

Solve for x

$$x=\frac{\left(\sqrt{y}+4\right)^{2}}{25}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$5\sqrt{x}-\sqrt{y}-\left(-\sqrt{y}\right)=4-\left(-\sqrt{y}\right)$$

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

$$5\sqrt{x}=4-\left(-\sqrt{y}\right)$$

Subtract -\sqrt{y} from 4.

$$5\sqrt{x}=\sqrt{y}+4$$

Divide both sides by 5.

$$\frac{5\sqrt{x}}{5}=\frac{\sqrt{y}+4}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$\sqrt{x}=\frac{\sqrt{y}+4}{5}$$

Square both sides of the equation.

$$x=\frac{\left(\sqrt{y}+4\right)^{2}}{25}$$

Solve for y

$$y=\left(5\sqrt{x}-4\right)^{2}$$

$$x\geq 0\text{ and }5\sqrt{x}-4\geq 0$$

Steps for Solving Radical Equations

Subtract 5\sqrt{x} from both sides of the equation.

$$-\sqrt{y}+5\sqrt{x}-5\sqrt{x}=4-5\sqrt{x}$$

Subtracting 5\sqrt{x} from itself leaves 0.

$$-\sqrt{y}=4-5\sqrt{x}$$

Subtract 5\sqrt{x} from 4.

$$-\sqrt{y}=-5\sqrt{x}+4$$

Divide both sides by -1.

$$\frac{-\sqrt{y}}{-1}=\frac{-5\sqrt{x}+4}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\sqrt{y}=\frac{-5\sqrt{x}+4}{-1}$$

Divide 4-5\sqrt{x} by -1.

$$\sqrt{y}=5\sqrt{x}-4$$

Square both sides of the equation.

$$y=\left(5\sqrt{x}-4\right)^{2}$$

Solve for x (complex solution)

$$x=\frac{\left(\sqrt{y}+4\right)^{2}}{25}$$

$$arg(\frac{\sqrt{y}+4}{5})<\pi$$

Solve for y (complex solution)

$$y=\left(5\sqrt{x}-4\right)^{2}$$

$$x=\frac{16}{25}\text{ or }arg(5\sqrt{x}-4)<\pi$$