Solve 62sqrt{x-2/3}+4=x55

$$62 \sqrt{ x- \frac{ 2 }{ 3 } } +4 = x55$$

Solve for x

$$x=\frac{\left(4-x_{55}\right)^{2}}{3844}+\frac{2}{3}$$

$$\frac{x_{55}}{62}-\frac{2}{31}\geq 0$$

Steps for Solving Radical Equations

Subtract 4 from both sides of the equation.

$$62\sqrt{x-\frac{2}{3}}+4-4=x_{55}-4$$

Subtracting 4 from itself leaves 0.

$$62\sqrt{x-\frac{2}{3}}=x_{55}-4$$

Divide both sides by 62.

$$\frac{62\sqrt{x-\frac{2}{3}}}{62}=\frac{x_{55}-4}{62}$$

Dividing by 62 undoes the multiplication by 62.

$$\sqrt{x-\frac{2}{3}}=\frac{x_{55}-4}{62}$$

Divide x_{55}-4 by 62.

$$\sqrt{x-\frac{2}{3}}=\frac{x_{55}}{62}-\frac{2}{31}$$

Square both sides of the equation.

$$x-\frac{2}{3}=\frac{\left(x_{55}-4\right)^{2}}{3844}$$

Add \frac{2}{3} to both sides of the equation.

$$x-\frac{2}{3}-\left(-\frac{2}{3}\right)=\frac{\left(x_{55}-4\right)^{2}}{3844}-\left(-\frac{2}{3}\right)$$

Subtracting -\frac{2}{3} from itself leaves 0.

$$x=\frac{\left(x_{55}-4\right)^{2}}{3844}-\left(-\frac{2}{3}\right)$$

Subtract -\frac{2}{3} from \frac{\left(-4+x_{55}\right)^{2}}{3844}.

$$x=\frac{\left(x_{55}-4\right)^{2}}{3844}+\frac{2}{3}$$

Solve for x (complex solution)

$$x=\frac{\left(4-x_{55}\right)^{2}}{3844}+\frac{2}{3}$$

$$x_{55}=4\text{ or }arg(-\frac{x_{55}}{62}+\frac{2}{31})\geq \pi$$

Solve for x_55 (complex solution)

$$x_{55}=\frac{62\sqrt{9x-6}}{3}+4$$

Solve for x_55

$$x_{55}=\frac{62\sqrt{9x-6}}{3}+4$$

$$x\geq \frac{2}{3}$$