Solve frac{3sqrt{2}}{2}=sqrt{18-a}

$$\frac { 3 \sqrt { 2 } } { 2 } = \sqrt { 18 - a }$$

Solve for a

$$a = \frac{27}{2} = 13\frac{1}{2} = 13.5$$

Steps for Solving Radical Equations

Multiply both sides of the equation by 2.

$$3\sqrt{2}=2\sqrt{18-a}$$

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

$$2\sqrt{18-a}=3\sqrt{2}$$

Divide both sides by 2.

$$\frac{2\sqrt{-a+18}}{2}=\frac{3\sqrt{2}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\sqrt{-a+18}=\frac{3\sqrt{2}}{2}$$

Square both sides of the equation.

$$-a+18=\frac{9}{2}$$

Subtract 18 from both sides of the equation.

$$-a+18-18=\frac{9}{2}-18$$

Subtracting 18 from itself leaves 0.

$$-a=\frac{9}{2}-18$$

Subtract 18 from \frac{9}{2}.

$$-a=-\frac{27}{2}$$

Divide both sides by -1.

$$\frac{-a}{-1}=-\frac{\frac{27}{2}}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=-\frac{\frac{27}{2}}{-1}$$

Divide -\frac{27}{2} by -1.

$$a=\frac{27}{2}$$