Solve 5sqrt{2x-7}=10

$$5 \sqrt { 2 x - 7 } = 10$$

Solve for x

$$x = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

Steps for Solving Radical Equations

Divide both sides by 5.

$$\frac{5\sqrt{2x-7}}{5}=\frac{10}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$\sqrt{2x-7}=\frac{10}{5}$$

Divide 10 by 5.

$$\sqrt{2x-7}=2$$

Square both sides of the equation.

$$2x-7=4$$

Add 7 to both sides of the equation.

$$2x-7-\left(-7\right)=4-\left(-7\right)$$

Subtracting -7 from itself leaves 0.

$$2x=4-\left(-7\right)$$

Subtract -7 from 4.

$$2x=11$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{11}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{11}{2}$$