Solve y=sqrt{ax}+b

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

Solve for a

$$\left\{\begin{matrix}a=\frac{\left(y-b\right)^{2}}{x}\text{, }&y-b\geq 0\text{ and }x\neq 0\\a\in \mathrm{R}\text{, }&y=b\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Radical Equations

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

$$\sqrt{ax}+b=y$$

Subtract b from both sides.

$$\sqrt{ax}=y-b$$

Square both sides of the equation.

$$xa=\left(y-b\right)^{2}$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{\left(y-b\right)^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{\left(y-b\right)^{2}}{x}$$

Solve for b

$$b=-\sqrt{ax}+y$$

$$\left(x\geq 0\text{ and }a\geq 0\right)\text{ or }\left(a\leq 0\text{ and }x\leq 0\right)$$