Solve y=sqrt{a-x}

$$y = \sqrt { a - x }$$

Solve for a

$$a=x+y^{2}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{a-x}=y$$

Square both sides of the equation.

$$a-x=y^{2}$$

Subtract -x from both sides of the equation.

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

Subtracting -x from itself leaves 0.

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

Subtract -x from y^{2}.

$$a=x+y^{2}$$

Solve for x

$$x=a-y^{2}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{a-x}=y$$

Square both sides of the equation.

$$-x+a=y^{2}$$

Subtract a from both sides of the equation.

$$-x+a-a=y^{2}-a$$

Subtracting a from itself leaves 0.

$$-x=y^{2}-a$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide y^{2}-a by -1.

$$x=a-y^{2}$$

Solve for a (complex solution)

$$a=x+y^{2}$$

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

Solve for x (complex solution)

$$x=a-y^{2}$$

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