How to solve z=(sqrt(2x))/(3y)

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve z=(sqrt(2x))/(3y) | Equatix

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Question

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

Solve for x

$x=\frac{9\left(yz\right)^{2}}{2}$
$\left(z\leq 0\text{ and }y<0\right)\text{ or }\left(z\geq 0\text{ and }y>0\right)$

Steps for Solving Radical Equations

Multiply both sides of the equation by $3y$.

$$z\times 3y=\sqrt{2x}$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{2x}=z\times 3y$$

Square both sides of the equation.

$$2x=9y^{2}z^{2}$$

Divide both sides by $2$.

$$\frac{2x}{2}=\frac{9y^{2}z^{2}}{2}$$

Dividing by $2$ undoes the multiplication by $2$.

$$x=\frac{9y^{2}z^{2}}{2}$$

Show Solution

Solve for y

$\left\{\begin{matrix}y=\frac{\sqrt{2x}}{3z}\text{, }&z\neq 0\text{ and }x>0\\y\neq 0\text{, }&x=0\text{ and }z=0\end{matrix}\right.$

Steps for Solving Linear Equation

Variable $y$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $3y$.

$$z\times 3y=\sqrt{2x}$$

Reorder the terms.

$$3yz=\sqrt{2x}$$

The equation is in standard form.

$$3zy=\sqrt{2x}$$

Divide both sides by $3z$.

$$\frac{3zy}{3z}=\frac{\sqrt{2x}}{3z}$$

Dividing by $3z$ undoes the multiplication by $3z$.

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

Variable $y$ cannot be equal to $0$.

$$y=\frac{\sqrt{2x}}{3z}\text{, }y\neq 0$$