Solve 2sqrt{x-3/4}-(1+1/2)^2=3

$$2 \sqrt { x - \frac { 3 } { 4 } } - ( 1 + \frac { 1 } { 2 } ) ^ { 2 } = 3$$

Solve for x

$$x = \frac{489}{64} = 7\frac{41}{64} = 7.640625$$

Steps for Solving Radical Equations

Add \frac{9}{4} to both sides of the equation.

$$2\sqrt{x-\frac{3}{4}}-\frac{9}{4}-\left(-\frac{9}{4}\right)=3-\left(-\frac{9}{4}\right)$$

Subtracting -\frac{9}{4} from itself leaves 0.

$$2\sqrt{x-\frac{3}{4}}=3-\left(-\frac{9}{4}\right)$$

Subtract -\frac{9}{4} from 3.

$$2\sqrt{x-\frac{3}{4}}=\frac{21}{4}$$

Divide both sides by 2.

$$\frac{2\sqrt{x-\frac{3}{4}}}{2}=\frac{\frac{21}{4}}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\sqrt{x-\frac{3}{4}}=\frac{\frac{21}{4}}{2}$$

Divide \frac{21}{4} by 2.

$$\sqrt{x-\frac{3}{4}}=\frac{21}{8}$$

Square both sides of the equation.

$$x-\frac{3}{4}=\frac{441}{64}$$

Add \frac{3}{4} to both sides of the equation.

$$x-\frac{3}{4}-\left(-\frac{3}{4}\right)=\frac{441}{64}-\left(-\frac{3}{4}\right)$$

Subtracting -\frac{3}{4} from itself leaves 0.

$$x=\frac{441}{64}-\left(-\frac{3}{4}\right)$$

Subtract -\frac{3}{4} from \frac{441}{64} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{489}{64}$$