Solve left(x+7.5right)^2+{left(sqrt{47.25}right)}^2=0

$${ \left(x+7.5 \right) }^{ 2 } + { \left( \sqrt{ 47.25 } \right) }^{ 2 } = 0$$

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

Subtracting \left(\sqrt{47.25}\right)^{2} from itself leaves 0.

$$\left(x+7.5\right)^{2}=-\left(\sqrt{47.25}\right)^{2}$$

Subtract \left(\sqrt{47.25}\right)^{2} from 0.

$$\left(x+7.5\right)^{2}=-47.25$$

Take the square root of both sides of the equation.

$$x+7.5=\frac{3\sqrt{21}i}{2} x+7.5=-\frac{3\sqrt{21}i}{2}$$

Subtract 7.5 from both sides of the equation.

$$x+7.5-7.5=\frac{3\sqrt{21}i}{2}-7.5 x+7.5-7.5=-\frac{3\sqrt{21}i}{2}-7.5$$

Subtracting 7.5 from itself leaves 0.

$$x=\frac{3\sqrt{21}i}{2}-7.5 x=-\frac{3\sqrt{21}i}{2}-7.5$$

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.

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