Solve y=sqrt{4-7x}

$$y= \sqrt{ 4-7x }$$

Solve for x

$$x=\frac{4-y^{2}}{7}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{4-7x}=y$$

Square both sides of the equation.

$$-7x+4=y^{2}$$

Subtract 4 from both sides of the equation.

$$-7x+4-4=y^{2}-4$$

Subtracting 4 from itself leaves 0.

$$-7x=y^{2}-4$$

Divide both sides by -7.

$$\frac{-7x}{-7}=\frac{y^{2}-4}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$x=\frac{y^{2}-4}{-7}$$

Divide y^{2}-4 by -7.

$$x=\frac{4-y^{2}}{7}$$

Solve for x (complex solution)

$$x=\frac{4-y^{2}}{7}$$

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

Solve for y

$$y=\sqrt{4-7x}$$

$$x\leq \frac{4}{7}$$