Solve y=sqrt{x}b

$$y = \sqrt { x } b$$

Solve for b

$$\left\{\begin{matrix}b=\frac{y}{\sqrt{x}}\text{, }&x>0\\b\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$\sqrt{x}b=y$$

Divide both sides by \sqrt{x}.

$$\frac{\sqrt{x}b}{\sqrt{x}}=\frac{y}{\sqrt{x}}$$

Dividing by \sqrt{x} undoes the multiplication by \sqrt{x}.

$$b=\frac{y}{\sqrt{x}}$$

Solve for x

$$\left\{\begin{matrix}x=\left(\frac{y}{b}\right)^{2}\text{, }&\left(y\geq 0\text{ and }b>0\right)\text{ or }\left(y\leq 0\text{ and }b<0\right)\\x\geq 0\text{, }&y=0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$\sqrt{x}b=y$$

Divide both sides by b.

$$\frac{b\sqrt{x}}{b}=\frac{y}{b}$$

Dividing by b undoes the multiplication by b.

$$\sqrt{x}=\frac{y}{b}$$

Square both sides of the equation.

$$x=\frac{y^{2}}{b^{2}}$$