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

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

Solve for x

$$x=\sqrt{2}-2\approx -0.585786438$$

$$x=-\sqrt{2}-2\approx -3.414213562$$

Steps by Finding Square Root

Subtract 2 from both sides of the equation.

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

Subtracting 2 from itself leaves 0.

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

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

Divide -2 by -1.

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

Take the square root of both sides of the equation.

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

Subtract 2 from both sides of the equation.

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

Subtracting 2 from itself leaves 0.

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