Solve (sqrt{x}sqrt{3})-14/2+1/2=0.5

$$( \sqrt { x } \sqrt { 3 } ) - \frac { 14 } { 2 } + \frac { 1 } { 2 } = 0.5$$

Solve for x

$$x = \frac{49}{3} = 16\frac{1}{3} \approx 16.333333333$$

Steps for Solving Radical Equations

Add \frac{13}{2} to both sides of the equation.

$$\sqrt{3}\sqrt{x}-\frac{13}{2}-\left(-\frac{13}{2}\right)=\frac{1}{2}-\left(-\frac{13}{2}\right)$$

Subtracting -\frac{13}{2} from itself leaves 0.

$$\sqrt{3}\sqrt{x}=\frac{1}{2}-\left(-\frac{13}{2}\right)$$

Subtract -\frac{13}{2} from \frac{1}{2} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\sqrt{3}\sqrt{x}=7$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}\sqrt{x}}{\sqrt{3}}=\frac{7}{\sqrt{3}}$$

Dividing by \sqrt{3} undoes the multiplication by \sqrt{3}.

$$\sqrt{x}=\frac{7}{\sqrt{3}}$$

Divide 7 by \sqrt{3}.

$$\sqrt{x}=\frac{7\sqrt{3}}{3}$$

Square both sides of the equation.

$$x=\frac{49}{3}$$