Solve y=sqrt{8x+1}

$$y = \sqrt { 8 x + 1 }$$

Solve for x

$$x=\frac{y^{2}-1}{8}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{8x+1}=y$$

Square both sides of the equation.

$$8x+1=y^{2}$$

Subtract 1 from both sides of the equation.

$$8x+1-1=y^{2}-1$$

Subtracting 1 from itself leaves 0.

$$8x=y^{2}-1$$

Divide both sides by 8.

$$\frac{8x}{8}=\frac{y^{2}-1}{8}$$

Dividing by 8 undoes the multiplication by 8.

$$x=\frac{y^{2}-1}{8}$$

Solve for x (complex solution)

$$x=\frac{y^{2}-1}{8}$$

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

Solve for y

$$y=\sqrt{8x+1}$$

$$x\geq -\frac{1}{8}$$