Solve (x-2)^2=-0.125

$$( x - 2 ) ^ { 2 } = - 0.125$$

Solve for x (complex solution)

$$x=-\frac{i\sqrt{2}}{4}+2\approx 2-0.353553391i$$

$$x=\frac{i\sqrt{2}}{4}+2\approx 2+0.353553391i$$

Steps by Finding Square Root

Add 2 to both sides of the equation.

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

Subtracting -2 from itself leaves 0.

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

Subtract -2 from \frac{i\sqrt{2}}{4}.

$$x=\frac{\sqrt{2}i}{4}+2$$

Subtract -2 from -\frac{i\sqrt{2}}{4}.

$$x=-\frac{\sqrt{2}i}{4}+2$$

The equation is now solved.

$$x=\frac{\sqrt{2}i}{4}+2 x=-\frac{\sqrt{2}i}{4}+2$$