Solve y=sqrt{21x-32}

$$y = \sqrt { 21 x - 32 }$$

Solve for x

$$x=\frac{y^{2}+32}{21}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{21x-32}=y$$

Square both sides of the equation.

$$21x-32=y^{2}$$

Add 32 to both sides of the equation.

$$21x-32-\left(-32\right)=y^{2}-\left(-32\right)$$

Subtracting -32 from itself leaves 0.

$$21x=y^{2}-\left(-32\right)$$

Subtract -32 from y^{2}.

$$21x=y^{2}+32$$

Divide both sides by 21.

$$\frac{21x}{21}=\frac{y^{2}+32}{21}$$

Dividing by 21 undoes the multiplication by 21.

$$x=\frac{y^{2}+32}{21}$$

Solve for x (complex solution)

$$x=\frac{y^{2}+32}{21}$$

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

Solve for y

$$y=\sqrt{21x-32}$$

$$x\geq \frac{32}{21}$$