Solve (x-6.5)^2=-24.25

$$( x - 6.5 ) ^ { 2 } = - 24.25$$

Solve for x (complex solution)

$$x=\frac{-i\sqrt{97}+13}{2}\approx 6.5-4.924428901i$$

$$x=\frac{13+i\sqrt{97}}{2}\approx 6.5+4.924428901i$$

Steps by Finding Square Root

Add 6.5 to both sides of the equation.

$$x-6.5-\left(-6.5\right)=\frac{\sqrt{97}i}{2}-\left(-6.5\right) x-6.5-\left(-6.5\right)=-\frac{\sqrt{97}i}{2}-\left(-6.5\right)$$

Subtracting -6.5 from itself leaves 0.

$$x=\frac{\sqrt{97}i}{2}-\left(-6.5\right) x=-\frac{\sqrt{97}i}{2}-\left(-6.5\right)$$

Subtract -6.5 from \frac{i\sqrt{97}}{2}.

$$x=\frac{13+\sqrt{97}i}{2}$$

Subtract -6.5 from -\frac{i\sqrt{97}}{2}.

$$x=\frac{-\sqrt{97}i+13}{2}$$

The equation is now solved.

$$x=\frac{13+\sqrt{97}i}{2} x=\frac{-\sqrt{97}i+13}{2}$$