Solve sqrt{2x-5/10}=10

$$\sqrt { \frac { 2 x - 5 } { 10 } } = 10$$

Solve for x

$$x = \frac{1005}{2} = 502\frac{1}{2} = 502.5$$

Steps for Solving Radical Equations

Divide each term of 2x-5 by 10 to get \frac{1}{5}x-\frac{1}{2}.

$$\sqrt{\frac{1}{5}x-\frac{1}{2}}=10$$

Square both sides of the equation.

$$\frac{1}{5}x-\frac{1}{2}=100$$

Add \frac{1}{2} to both sides of the equation.

$$\frac{1}{5}x-\frac{1}{2}-\left(-\frac{1}{2}\right)=100-\left(-\frac{1}{2}\right)$$

Subtracting -\frac{1}{2} from itself leaves 0.

$$\frac{1}{5}x=100-\left(-\frac{1}{2}\right)$$

Subtract -\frac{1}{2} from 100.

$$\frac{1}{5}x=\frac{201}{2}$$

Multiply both sides by 5.

$$\frac{\frac{1}{5}x}{\frac{1}{5}}=\frac{\frac{201}{2}}{\frac{1}{5}}$$

Dividing by \frac{1}{5} undoes the multiplication by \frac{1}{5}.

$$x=\frac{\frac{201}{2}}{\frac{1}{5}}$$

Divide \frac{201}{2} by \frac{1}{5} by multiplying \frac{201}{2} by the reciprocal of \frac{1}{5}.

$$x=\frac{1005}{2}$$