Solve Nu^2=y

$$N u ^ { 2 } = y$$

Solve for N (complex solution)

$$\left\{\begin{matrix}N=\frac{y}{u^{2}}\text{, }&u\neq 0\\N\in \mathrm{C}\text{, }&y=0\text{ and }u=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$u^{2}N=y$$

Divide both sides by u^{2}.

$$\frac{u^{2}N}{u^{2}}=\frac{y}{u^{2}}$$

Dividing by u^{2} undoes the multiplication by u^{2}.

$$N=\frac{y}{u^{2}}$$

Solve for N

$$\left\{\begin{matrix}N=\frac{y}{u^{2}}\text{, }&u\neq 0\\N\in \mathrm{R}\text{, }&y=0\text{ and }u=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$u^{2}N=y$$

Divide both sides by u^{2}.

$$\frac{u^{2}N}{u^{2}}=\frac{y}{u^{2}}$$

Dividing by u^{2} undoes the multiplication by u^{2}.

$$N=\frac{y}{u^{2}}$$

Solve for u (complex solution)

$$\left\{\begin{matrix}u=-N^{-\frac{1}{2}}\sqrt{y}\text{; }u=N^{-\frac{1}{2}}\sqrt{y}\text{, }&N\neq 0\\u\in \mathrm{C}\text{, }&y=0\text{ and }N=0\end{matrix}\right.$$

Solve for u

$$\left\{\begin{matrix}u=\sqrt{\frac{y}{N}}\text{; }u=-\sqrt{\frac{y}{N}}\text{, }&\left(y\geq 0\text{ and }N>0\right)\text{ or }\left(y\leq 0\text{ and }N<0\right)\\u\in \mathrm{R}\text{, }&y=0\text{ and }N=0\end{matrix}\right.$$