Solve 4left(x+1right)^2+9=0

$$4 { \left(x+1 \right) }^{ 2 } +9=0$$

Solve for x (complex solution)

$$x=-1-\frac{3}{2}i=-1-1.5i$$

$$x=-1+\frac{3}{2}i=-1+1.5i$$

Steps by Finding Square Root

Subtracting 9 from itself leaves 0.

$$4\left(x+1\right)^{2}=-9$$

Divide both sides by 4.

$$\frac{4\left(x+1\right)^{2}}{4}=-\frac{9}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$\left(x+1\right)^{2}=-\frac{9}{4}$$

Take the square root of both sides of the equation.

$$x+1=\frac{3}{2}i x+1=-\frac{3}{2}i$$

Subtract 1 from both sides of the equation.

$$x+1-1=\frac{3}{2}i-1 x+1-1=-\frac{3}{2}i-1$$

Subtracting 1 from itself leaves 0.

$$x=\frac{3}{2}i-1 x=-\frac{3}{2}i-1$$

Subtract 1 from \frac{3}{2}i.

$$x=-1+\frac{3}{2}i$$

Subtract 1 from -\frac{3}{2}i.

$$x=-1-\frac{3}{2}i$$

The equation is now solved.

$$x=-1+\frac{3}{2}i x=-1-\frac{3}{2}i$$