Solve left(x+2right)^2+53=0

$${ \left(x+2 \right) }^{ 2 } +53 = 0$$

Solve for x (complex solution)

$$x=-\sqrt{53}i-2\approx -2-7.280109889i$$

$$x=-2+\sqrt{53}i\approx -2+7.280109889i$$

Steps by Finding Square Root

Subtracting 53 from itself leaves 0.

$$\left(x+2\right)^{2}=-53$$

Take the square root of both sides of the equation.

$$x+2=\sqrt{53}i x+2=-\sqrt{53}i$$

Subtract 2 from both sides of the equation.

$$x+2-2=\sqrt{53}i-2 x+2-2=-\sqrt{53}i-2$$

Subtracting 2 from itself leaves 0.

$$x=\sqrt{53}i-2 x=-\sqrt{53}i-2$$

Subtract 2 from i\sqrt{53}.

$$x=-2+\sqrt{53}i$$

Subtract 2 from -i\sqrt{53}.

$$x=-\sqrt{53}i-2$$

The equation is now solved.

$$x=-2+\sqrt{53}i x=-\sqrt{53}i-2$$