Solve 2+(1/2-x)^2=0.25

$$2 + ( \frac { 1 } { 2 } - x ) ^ { 2 } = 0.25$$

Solve for x (complex solution)

$$x=\frac{1+i\sqrt{7}}{2}\approx 0.5+1.322875656i$$

$$x=\frac{-i\sqrt{7}+1}{2}\approx 0.5-1.322875656i$$

Steps by Finding Square Root

Subtracting 2 from itself leaves 0.

$$\left(-x+\frac{1}{2}\right)^{2}=0.25-2$$

Subtract 2 from 0.25.

$$\left(-x+\frac{1}{2}\right)^{2}=-1.75$$

Take the square root of both sides of the equation.

$$-x+\frac{1}{2}=\frac{\sqrt{7}i}{2} -x+\frac{1}{2}=-\frac{\sqrt{7}i}{2}$$

Subtract \frac{1}{2} from both sides of the equation.

$$-x+\frac{1}{2}-\frac{1}{2}=\frac{\sqrt{7}i}{2}-\frac{1}{2} -x+\frac{1}{2}-\frac{1}{2}=-\frac{\sqrt{7}i}{2}-\frac{1}{2}$$

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

$$-x=\frac{\sqrt{7}i}{2}-\frac{1}{2} -x=-\frac{\sqrt{7}i}{2}-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{i\sqrt{7}}{2}.

$$-x=\frac{-1+\sqrt{7}i}{2}$$

Subtract \frac{1}{2} from -\frac{i\sqrt{7}}{2}.

$$-x=\frac{-\sqrt{7}i-1}{2}$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{-1+\sqrt{7}i}{-2} \frac{-x}{-1}=\frac{-\sqrt{7}i-1}{-2}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{-1+\sqrt{7}i}{-2} x=\frac{-\sqrt{7}i-1}{-2}$$

Divide \frac{i\sqrt{7}-1}{2} by -1.

$$x=\frac{-\sqrt{7}i+1}{2}$$

Divide \frac{-i\sqrt{7}-1}{2} by -1.

$$x=\frac{1+\sqrt{7}i}{2}$$

The equation is now solved.

$$x=\frac{-\sqrt{7}i+1}{2} x=\frac{1+\sqrt{7}i}{2}$$