Solve -left(x-2right)^2+3.5=0

$$- { \left(x-2 \right) }^{ 2 } +3.5 = 0$$

Solve for x

$$x=\frac{\sqrt{14}}{2}+2\approx 3.870828693$$

$$x=-\frac{\sqrt{14}}{2}+2\approx 0.129171307$$

Steps by Finding Square Root

Subtract 3.5 from both sides of the equation.

$$-\left(x-2\right)^{2}+3.5-3.5=-3.5$$

Subtracting 3.5 from itself leaves 0.

$$-\left(x-2\right)^{2}=-3.5$$

Divide both sides by -1.

$$\frac{-\left(x-2\right)^{2}}{-1}=-\frac{3.5}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$\left(x-2\right)^{2}=-\frac{3.5}{-1}$$

Divide -3.5 by -1.

$$\left(x-2\right)^{2}=3.5$$

Take the square root of both sides of the equation.

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

Add 2 to both sides of the equation.

$$x-2-\left(-2\right)=\frac{\sqrt{14}}{2}-\left(-2\right) x-2-\left(-2\right)=-\frac{\sqrt{14}}{2}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$x=\frac{\sqrt{14}}{2}-\left(-2\right) x=-\frac{\sqrt{14}}{2}-\left(-2\right)$$

Subtract -2 from \frac{\sqrt{14}}{2}.

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

Subtract -2 from -\frac{\sqrt{14}}{2}.

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

The equation is now solved.

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