Solve (x-9/2)^2=3

$$( x - \frac { 9 } { 2 } ) ^ { 2 } = 3$$

Solve for x

$$x=\sqrt{3}+\frac{9}{2}\approx 6.232050808$$

$$x=\frac{9}{2}-\sqrt{3}\approx 2.767949192$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-\frac{9}{2}=\sqrt{3} x-\frac{9}{2}=-\sqrt{3}$$

Add \frac{9}{2} to both sides of the equation.

$$x-\frac{9}{2}-\left(-\frac{9}{2}\right)=\sqrt{3}-\left(-\frac{9}{2}\right) x-\frac{9}{2}-\left(-\frac{9}{2}\right)=-\sqrt{3}-\left(-\frac{9}{2}\right)$$

Subtracting -\frac{9}{2} from itself leaves 0.

$$x=\sqrt{3}-\left(-\frac{9}{2}\right) x=-\sqrt{3}-\left(-\frac{9}{2}\right)$$

Subtract -\frac{9}{2} from \sqrt{3}.

$$x=\sqrt{3}+\frac{9}{2}$$

Subtract -\frac{9}{2} from -\sqrt{3}.

$$x=\frac{9}{2}-\sqrt{3}$$

The equation is now solved.

$$x=\sqrt{3}+\frac{9}{2} x=\frac{9}{2}-\sqrt{3}$$