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

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

Solve for x (complex solution)

$$x=-\frac{5\sqrt{10}i}{4}-1\approx -1-3.952847075i$$

$$x=\frac{5\sqrt{10}i}{4}-1\approx -1+3.952847075i$$

Steps by Finding Square Root

Dividing by 2 undoes the multiplication by 2.

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

Divide -\frac{125}{4} by 2.

$$\left(x+1\right)^{2}=-\frac{125}{8}$$

Take the square root of both sides of the equation.

$$x+1=\frac{5\sqrt{10}i}{4} x+1=-\frac{5\sqrt{10}i}{4}$$

Subtract 1 from both sides of the equation.

$$x+1-1=\frac{5\sqrt{10}i}{4}-1 x+1-1=-\frac{5\sqrt{10}i}{4}-1$$

Subtracting 1 from itself leaves 0.

$$x=\frac{5\sqrt{10}i}{4}-1 x=-\frac{5\sqrt{10}i}{4}-1$$