Solve -4xsqrt{xy}=1

$$-4x \sqrt{ xy } = 1$$

Solve for y

$$y=\frac{1}{16x^{3}}$$

$$x<0$$

Steps for Solving Radical Equations

Divide both sides by -4x.

$$\frac{\left(-4x\right)\sqrt{xy}}{-4x}=\frac{1}{-4x}$$

Dividing by -4x undoes the multiplication by -4x.

$$\sqrt{xy}=\frac{1}{-4x}$$

Divide 1 by -4x.

$$\sqrt{xy}=-\frac{1}{4x}$$

Square both sides of the equation.

$$xy=\frac{1}{16x^{2}}$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{1}{16x^{2}x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{1}{16x^{2}x}$$

Divide \frac{1}{16x^{2}} by x.

$$y=\frac{1}{16x^{3}}$$

Solve for x (complex solution)

$$x=\frac{2^{\frac{2}{3}}e^{\frac{2\pi i}{3}}y^{-\frac{1}{3}}}{4}$$

$$y\neq 0$$

Solve for y (complex solution)

$$y=\frac{1}{16x^{3}}$$

$$|-\pi +arg(\sqrt{\frac{1}{x^{2}}}x)|<\pi \text{ and }x\neq 0$$

Solve for x

$$x=\frac{2^{\frac{2}{3}}}{4\sqrt[3]{y}}$$

$$y<0$$