Solve y=sqrt{10ux+1}

$$y = \sqrt { 10 u x + 1 }$$

Solve for u

$$\left\{\begin{matrix}u=-\frac{1-y^{2}}{10x}\text{, }&y\geq 0\text{ and }x\neq 0\\u\in \mathrm{R}\text{, }&y=1\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$\sqrt{10ux+1}=y$$

Square both sides of the equation.

$$10xu+1=y^{2}$$

Subtract 1 from both sides of the equation.

$$10xu+1-1=y^{2}-1$$

Subtracting 1 from itself leaves 0.

$$10xu=y^{2}-1$$

Divide both sides by 10x.

$$\frac{10xu}{10x}=\frac{y^{2}-1}{10x}$$

Dividing by 10x undoes the multiplication by 10x.

$$u=\frac{y^{2}-1}{10x}$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{1-y^{2}}{10u}\text{, }&y\geq 0\text{ and }u\neq 0\\x\in \mathrm{R}\text{, }&y=1\text{ and }u=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$\sqrt{10ux+1}=y$$

Square both sides of the equation.

$$10ux+1=y^{2}$$

Subtract 1 from both sides of the equation.

$$10ux+1-1=y^{2}-1$$

Subtracting 1 from itself leaves 0.

$$10ux=y^{2}-1$$

Divide both sides by 10u.

$$\frac{10ux}{10u}=\frac{y^{2}-1}{10u}$$

Dividing by 10u undoes the multiplication by 10u.

$$x=\frac{y^{2}-1}{10u}$$

Solve for u (complex solution)

$$\left\{\begin{matrix}u=-\frac{1-y^{2}}{10x}\text{, }&x\neq 0\text{ and }\left(y=0\text{ or }arg(y)<\pi \right)\\u\in \mathrm{C}\text{, }&y=1\text{ and }x=0\end{matrix}\right.$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{1-y^{2}}{10u}\text{, }&u\neq 0\text{ and }\left(y=0\text{ or }arg(y)<\pi \right)\\x\in \mathrm{C}\text{, }&y=1\text{ and }u=0\end{matrix}\right.$$