Solve (x-6.5)^2=21.25

$$( x - 6.5 ) ^ { 2 } = 21.25$$

Solve for x

$$x = \frac{\sqrt{85} + 13}{2} \approx 11.109772229$$

$$x = \frac{13 - \sqrt{85}}{2} \approx 1.890227771$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x-6.5=\frac{\sqrt{85}}{2} x-6.5=-\frac{\sqrt{85}}{2}$$

Add 6.5 to both sides of the equation.

$$x-6.5-\left(-6.5\right)=\frac{\sqrt{85}}{2}-\left(-6.5\right) x-6.5-\left(-6.5\right)=-\frac{\sqrt{85}}{2}-\left(-6.5\right)$$

Subtracting -6.5 from itself leaves 0.

$$x=\frac{\sqrt{85}}{2}-\left(-6.5\right) x=-\frac{\sqrt{85}}{2}-\left(-6.5\right)$$

Subtract -6.5 from \frac{\sqrt{85}}{2}.

$$x=\frac{\sqrt{85}+13}{2}$$

Subtract -6.5 from -\frac{\sqrt{85}}{2}.

$$x=\frac{13-\sqrt{85}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{85}+13}{2} x=\frac{13-\sqrt{85}}{2}$$