Solve (x+8.5)^2=-59.25

$$( x + 8.5 ) ^ { 2 } = - 59.25$$

Solve for x (complex solution)

$$x=\frac{-i\sqrt{237}-17}{2}\approx -8.5-7.697402159i$$

$$x=\frac{-17+i\sqrt{237}}{2}\approx -8.5+7.697402159i$$

Steps by Finding Square Root

Subtract 8.5 from both sides of the equation.

$$x+8.5-8.5=\frac{\sqrt{237}i}{2}-8.5 x+8.5-8.5=-\frac{\sqrt{237}i}{2}-8.5$$

Subtracting 8.5 from itself leaves 0.

$$x=\frac{\sqrt{237}i}{2}-8.5 x=-\frac{\sqrt{237}i}{2}-8.5$$

Subtract 8.5 from \frac{i\sqrt{237}}{2}.

$$x=\frac{-17+\sqrt{237}i}{2}$$

Subtract 8.5 from -\frac{i\sqrt{237}}{2}.

$$x=\frac{-\sqrt{237}i-17}{2}$$

The equation is now solved.

$$x=\frac{-17+\sqrt{237}i}{2} x=\frac{-\sqrt{237}i-17}{2}$$