How to solve z=sqrt((y3)/(x2))

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((y3)/(x2)) | Equatix

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$$z= \sqrt{ \frac{ y3 }{ x2 } }$$

$y_{3}=x_{2}z^{2}$
$z\geq 0\text{ and }x_{2}\neq 0$

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

$$\sqrt{\frac{y_{3}}{x_{2}}}=z$$

Square both sides of the equation.

$$\frac{1}{x_{2}}y_{3}=z^{2}$$

Divide both sides by $x_{2}^{-1}$.

$$\frac{\frac{1}{x_{2}}y_{3}x_{2}}{1}=\frac{z^{2}x_{2}}{1}$$

Dividing by $x_{2}^{-1}$ undoes the multiplication by $x_{2}^{-1}$.

$$y_{3}=\frac{z^{2}x_{2}}{1}$$

Divide $z^{2}$ by $x_{2}^{-1}$.

$$y_{3}=x_{2}z^{2}$$

$\left\{\begin{matrix}x_{2}=\frac{y_{3}}{z^{2}}\text{, }&z>0\text{ and }y_{3}\neq 0\\x_{2}\neq 0\text{, }&y_{3}=0\text{ and }z=0\end{matrix}\right.$