Solve y=sqrt{x}+3sqrt{x}

$$y = \sqrt { x } + 3 \sqrt { x }$$

Solve for x

$$x=\frac{y^{2}}{16}$$

$$y\geq 0$$

Steps for Solving Radical Equations

Combine \sqrt{x} and 3\sqrt{x} to get 4\sqrt{x}.

$$y=4\sqrt{x}$$

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

$$4\sqrt{x}=y$$

Divide both sides by 4.

$$\frac{4\sqrt{x}}{4}=\frac{y}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$\sqrt{x}=\frac{y}{4}$$

Square both sides of the equation.

$$x=\frac{y^{2}}{16}$$

Solve for x (complex solution)

$$x=\frac{y^{2}}{16}$$

$$arg(y)<\pi \text{ or }y=0$$

Solve for y (complex solution)

$$y=4\sqrt{x}$$

Solve for y

$$y=4\sqrt{x}$$

$$x\geq 0$$