Solve (x+2)^2+6=5/2

$$( x + 2 ) ^ { 2 } + 6 = \frac { 5 } { 2 }$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{14}i}{2}-2\approx -2-1.870828693i$$

$$x=\frac{\sqrt{14}i}{2}-2\approx -2+1.870828693i$$

Steps by Finding Square Root

Subtracting 6 from itself leaves 0.

$$\left(x+2\right)^{2}=\frac{5}{2}-6$$

Subtract 6 from \frac{5}{2}.

$$\left(x+2\right)^{2}=-\frac{7}{2}$$

Take the square root of both sides of the equation.

$$x+2=\frac{\sqrt{14}i}{2} x+2=-\frac{\sqrt{14}i}{2}$$

Subtract 2 from both sides of the equation.

$$x+2-2=\frac{\sqrt{14}i}{2}-2 x+2-2=-\frac{\sqrt{14}i}{2}-2$$

Subtracting 2 from itself leaves 0.

$$x=\frac{\sqrt{14}i}{2}-2 x=-\frac{\sqrt{14}i}{2}-2$$