Solve y=sqrt{5x+10}

$$y= \sqrt{ 5x+10 }$$

Solve for x

$$x=\frac{y^{2}-10}{5}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{5x+10}=y$$

Square both sides of the equation.

$$5x+10=y^{2}$$

Subtract 10 from both sides of the equation.

$$5x+10-10=y^{2}-10$$

Subtracting 10 from itself leaves 0.

$$5x=y^{2}-10$$

Divide both sides by 5.

$$\frac{5x}{5}=\frac{y^{2}-10}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x=\frac{y^{2}-10}{5}$$

Divide y^{2}-10 by 5.

$$x=\frac{y^{2}}{5}-2$$

Solve for x (complex solution)

$$x=\frac{y^{2}-10}{5}$$

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

Solve for y (complex solution)

$$y=\sqrt{5\left(x+2\right)}$$

Solve for y

$$y=\sqrt{5\left(x+2\right)}$$

$$x\geq -2$$