Solve y=sqrt{(2a+2-2b}

$$y = \sqrt { ( 2 a + 2 - 2 b }$$

Solve for a

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

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{2a+2-2b}=y$$

Square both sides of the equation.

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

Subtract 2-2b from both sides of the equation.

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

Subtracting 2-2b from itself leaves 0.

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

Subtract 2-2b from y^{2}.

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

Divide both sides by 2.

$$\frac{2a}{2}=\frac{y^{2}+2b-2}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$a=\frac{y^{2}+2b-2}{2}$$

Divide y^{2}-2+2b by 2.

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

Solve for b

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

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{2a+2-2b}=y$$

Square both sides of the equation.

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

Subtract 2+2a from both sides of the equation.

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

Subtracting 2+2a from itself leaves 0.

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

Subtract 2+2a from y^{2}.

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

Divide both sides by -2.

$$\frac{-2b}{-2}=\frac{y^{2}-2a-2}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$b=\frac{y^{2}-2a-2}{-2}$$

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

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