Solve (x-7.5)^2=-47.25

$$( x - 7.5 ) ^ { 2 } = - 47.25$$

Solve for x (complex solution)

$$x=\frac{-i\times 3\sqrt{21}+15}{2}\approx 7.5-6.873863542i$$

$$x=\frac{15+i\times 3\sqrt{21}}{2}\approx 7.5+6.873863542i$$

Steps by Finding Square Root

Add 7.5 to both sides of the equation.

$$x-7.5-\left(-7.5\right)=\frac{3\sqrt{21}i}{2}-\left(-7.5\right) x-7.5-\left(-7.5\right)=-\frac{3\sqrt{21}i}{2}-\left(-7.5\right)$$

Subtracting -7.5 from itself leaves 0.

$$x=\frac{3\sqrt{21}i}{2}-\left(-7.5\right) x=-\frac{3\sqrt{21}i}{2}-\left(-7.5\right)$$

Subtract -7.5 from \frac{3i\sqrt{21}}{2}.

$$x=\frac{15+3\sqrt{21}i}{2}$$

Subtract -7.5 from -\frac{3i\sqrt{21}}{2}.

$$x=\frac{-3\sqrt{21}i+15}{2}$$

The equation is now solved.

$$x=\frac{15+3\sqrt{21}i}{2} x=\frac{-3\sqrt{21}i+15}{2}$$