Solve (2)2(x-1)^2=-125/4

$$( 2 ) 2 ( x - 1 ) ^ { 2 } = - \frac { 125 } { 4 }$$

Solve for x (complex solution)

$$x=-\frac{5\sqrt{5}i}{4}+1\approx 1-2.795084972i$$

$$x=\frac{5\sqrt{5}i}{4}+1\approx 1+2.795084972i$$

Steps by Finding Square Root

Dividing by 4 undoes the multiplication by 4.

$$\left(x-1\right)^{2}=-\frac{\frac{125}{4}}{4}$$

Divide -\frac{125}{4} by 4.

$$\left(x-1\right)^{2}=-\frac{125}{16}$$

Take the square root of both sides of the equation.

$$x-1=\frac{5\sqrt{5}i}{4} x-1=-\frac{5\sqrt{5}i}{4}$$

Add 1 to both sides of the equation.

$$x-1-\left(-1\right)=\frac{5\sqrt{5}i}{4}-\left(-1\right) x-1-\left(-1\right)=-\frac{5\sqrt{5}i}{4}-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$x=\frac{5\sqrt{5}i}{4}-\left(-1\right) x=-\frac{5\sqrt{5}i}{4}-\left(-1\right)$$

Subtract -1 from \frac{5i\sqrt{5}}{4}.

$$x=\frac{5\sqrt{5}i}{4}+1$$

Subtract -1 from -\frac{5i\sqrt{5}}{4}.

$$x=-\frac{5\sqrt{5}i}{4}+1$$

The equation is now solved.

$$x=\frac{5\sqrt{5}i}{4}+1 x=-\frac{5\sqrt{5}i}{4}+1$$