Solve y=d(sqrt{x})

$$y = d ( \sqrt { x } )$$

Solve for d

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

Steps for Solving Linear Equation

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

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

The equation is in standard form.

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

Divide both sides by \sqrt{x}.

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

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

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

Solve for x

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

Steps for Solving Radical Equations

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

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

Divide both sides by d.

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

Dividing by d undoes the multiplication by d.

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

Square both sides of the equation.

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