Solve sqrt{x+1/4}-0.5=1

$$\sqrt{ x+ \frac{ 1 }{ 4 } } -0.5=1$$

Solve for x

$$x=2$$

Steps for Solving Radical Equations

Add 0.5 to both sides of the equation.

$$\sqrt{x+\frac{1}{4}}-0.5-\left(-0.5\right)=1-\left(-0.5\right)$$

Subtracting -0.5 from itself leaves 0.

$$\sqrt{x+\frac{1}{4}}=1-\left(-0.5\right)$$

Subtract -0.5 from 1.

$$\sqrt{x+\frac{1}{4}}=1.5$$

Square both sides of the equation.

$$x+\frac{1}{4}=2.25$$

Subtract \frac{1}{4} from both sides of the equation.

$$x+\frac{1}{4}-\frac{1}{4}=2.25-\frac{1}{4}$$

Subtracting \frac{1}{4} from itself leaves 0.

$$x=2.25-\frac{1}{4}$$

Subtract \frac{1}{4} from 2.25 by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=2$$