Solve -1/2(x+5)^2+2=0

$$- \frac { 1 } { 2 } ( x + 5 ) ^ { 2 } + 2 = 0$$

Solve for x

$$x=-3$$

$$x=-7$$

Steps by Finding Square Root

Subtract 2 from both sides of the equation.

$$-\frac{1}{2}\left(x+5\right)^{2}+2-2=-2$$

Subtracting 2 from itself leaves 0.

$$-\frac{1}{2}\left(x+5\right)^{2}=-2$$

Multiply both sides by -2.

$$\frac{-\frac{1}{2}\left(x+5\right)^{2}}{-\frac{1}{2}}=-\frac{2}{-\frac{1}{2}}$$

Dividing by -\frac{1}{2} undoes the multiplication by -\frac{1}{2}.

$$\left(x+5\right)^{2}=-\frac{2}{-\frac{1}{2}}$$

Divide -2 by -\frac{1}{2} by multiplying -2 by the reciprocal of -\frac{1}{2}.

$$\left(x+5\right)^{2}=4$$

Take the square root of both sides of the equation.

$$x+5=2 x+5=-2$$

Subtract 5 from both sides of the equation.

$$x+5-5=2-5 x+5-5=-2-5$$

Subtracting 5 from itself leaves 0.

$$x=2-5 x=-2-5$$

Subtract 5 from 2.

$$x=-3$$

Subtract 5 from -2.

$$x=-7$$

The equation is now solved.

$$x=-3 x=-7$$