Solve -1/2(x-2)^2+3=0

$$- \frac { 1 } { 2 } ( x - 2 ) ^ { 2 } + 3 = 0$$

Solve for x

$$x=\sqrt{6}+2\approx 4.449489743$$

$$x=2-\sqrt{6}\approx -0.449489743$$

Steps by Finding Square Root

Subtract 3 from both sides of the equation.

$$-\frac{1}{2}\left(x-2\right)^{2}+3-3=-3$$

Subtracting 3 from itself leaves 0.

$$-\frac{1}{2}\left(x-2\right)^{2}=-3$$

Multiply both sides by -2.

$$\frac{-\frac{1}{2}\left(x-2\right)^{2}}{-\frac{1}{2}}=-\frac{3}{-\frac{1}{2}}$$

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

$$\left(x-2\right)^{2}=-\frac{3}{-\frac{1}{2}}$$

Divide -3 by -\frac{1}{2} by multiplying -3 by the reciprocal of -\frac{1}{2}.

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

Take the square root of both sides of the equation.

$$x-2=\sqrt{6} x-2=-\sqrt{6}$$

Add 2 to both sides of the equation.

$$x-2-\left(-2\right)=\sqrt{6}-\left(-2\right) x-2-\left(-2\right)=-\sqrt{6}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$x=\sqrt{6}-\left(-2\right) x=-\sqrt{6}-\left(-2\right)$$

Subtract -2 from \sqrt{6}.

$$x=\sqrt{6}+2$$

Subtract -2 from -\sqrt{6}.

$$x=2-\sqrt{6}$$

The equation is now solved.

$$x=\sqrt{6}+2 x=2-\sqrt{6}$$