Solve y=1.3sqrt{x}+4.2

$$y = 1.3 \sqrt { x } + 4.2$$

Solve for x

$$x=\left(\frac{42-10y}{13}\right)^{2}$$

$$-\frac{42-10y}{13}\geq 0$$

Steps for Solving Radical Equations

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

$$1.3\sqrt{x}+4.2=y$$

Subtract 4.2 from both sides.

$$1.3\sqrt{x}=y-4.2$$

Divide both sides of the equation by 1.3, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{1.3\sqrt{x}}{1.3}=\frac{y-4.2}{1.3}$$

Dividing by 1.3 undoes the multiplication by 1.3.

$$\sqrt{x}=\frac{y-4.2}{1.3}$$

Divide y-4.2 by 1.3 by multiplying y-4.2 by the reciprocal of 1.3.

$$\sqrt{x}=\frac{10y-42}{13}$$

Square both sides of the equation.

$$x=\frac{4\left(5y-21\right)^{2}}{169}$$

Solve for x (complex solution)

$$x=\left(\frac{42-10y}{13}\right)^{2}$$

$$y=\frac{21}{5}\text{ or }arg(\frac{42-10y}{13})\geq \pi$$

Solve for y (complex solution)

$$y=\frac{13\sqrt{x}}{10}+4.2$$

Solve for y

$$y=\frac{13\sqrt{x}}{10}+4.2$$

$$x\geq 0$$