Solve 5.0*10^{3}=(9*10^9)(8.0*10^6)(-6*10^-6)/r^2

$$5.0 \times 10 ^ { 3 } = \frac { ( 9 \times 10 ^ { 9 } ) ( 8.0 \times 10 ^ { 6 } ) ( - 6 \times 10 ^ { - 6 } ) } { r ^ { 2 } }$$

Solve for r

$$r=-2400\sqrt{15}i\approx -0-9295.160030898i$$

$$r=2400\sqrt{15}i\approx 9295.160030898i$$

Steps by Finding Square Root

Variable r cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by r^{2}.

$$5\times 10^{3}r^{2}=9\times 10^{9}\times 8\times 10^{6}\left(-6\right)\times 10^{-6}$$

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$5\times 10^{3}r^{2}=9\times 10^{15}\times 8\left(-6\right)\times 10^{-6}$$

To multiply powers of the same base, add their exponents. Add 15 and -6 to get 9.

$$5\times 10^{3}r^{2}=9\times 10^{9}\times 8\left(-6\right)$$

Calculate 10 to the power of 3 and get 1000.

$$5\times 1000r^{2}=9\times 10^{9}\times 8\left(-6\right)$$

Multiply 5 and 1000 to get 5000.

$$5000r^{2}=9\times 10^{9}\times 8\left(-6\right)$$

Calculate 10 to the power of 9 and get 1000000000.

$$5000r^{2}=9\times 1000000000\times 8\left(-6\right)$$

Multiply 9 and 1000000000 to get 9000000000.

$$5000r^{2}=9000000000\times 8\left(-6\right)$$

Multiply 9000000000 and 8 to get 72000000000.

$$5000r^{2}=72000000000\left(-6\right)$$

Multiply 72000000000 and -6 to get -432000000000.

$$5000r^{2}=-432000000000$$

Divide both sides by 5000.

$$r^{2}=\frac{-432000000000}{5000}$$

Divide -432000000000 by 5000 to get -86400000.

$$r^{2}=-86400000$$

The equation is now solved.

$$r=2400\sqrt{15}i r=-2400\sqrt{15}i$$

Steps Using the Quadratic Formula

Variable r cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by r^{2}.

$$5\times 10^{3}r^{2}=9\times 10^{9}\times 8\times 10^{6}\left(-6\right)\times 10^{-6}$$

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$5\times 10^{3}r^{2}=9\times 10^{15}\times 8\left(-6\right)\times 10^{-6}$$

To multiply powers of the same base, add their exponents. Add 15 and -6 to get 9.

$$5\times 10^{3}r^{2}=9\times 10^{9}\times 8\left(-6\right)$$

Calculate 10 to the power of 3 and get 1000.

$$5\times 1000r^{2}=9\times 10^{9}\times 8\left(-6\right)$$

Multiply 5 and 1000 to get 5000.

$$5000r^{2}=9\times 10^{9}\times 8\left(-6\right)$$

Calculate 10 to the power of 9 and get 1000000000.

$$5000r^{2}=9\times 1000000000\times 8\left(-6\right)$$

Multiply 9 and 1000000000 to get 9000000000.

$$5000r^{2}=9000000000\times 8\left(-6\right)$$

Multiply 9000000000 and 8 to get 72000000000.

$$5000r^{2}=72000000000\left(-6\right)$$

Multiply 72000000000 and -6 to get -432000000000.

$$5000r^{2}=-432000000000$$

Add 432000000000 to both sides.

$$5000r^{2}[phone]=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5000 for a, 0 for b, and 432000000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 5000\times 432000000000}}{2\times 5000}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times 5000\times 432000000000}}{2\times 5000}$$

Multiply -4 times 5000.

$$r=\frac{0±\sqrt{-20000\times 432000000000}}{2\times 5000}$$

Multiply -20000 times 432000000000.

$$r=\frac{0±\sqrt{-8640000000000000}}{2\times 5000}$$

Take the square root of -8640000000000000.

$$r=\frac{0±24000000\sqrt{15}i}{2\times 5000}$$

Multiply 2 times 5000.

$$r=\frac{0±24000000\sqrt{15}i}{10000}$$

Now solve the equation r=\frac{0±24000000\sqrt{15}i}{10000} when ± is plus.

$$r=2400\sqrt{15}i$$

Now solve the equation r=\frac{0±24000000\sqrt{15}i}{10000} when ± is minus.

$$r=-2400\sqrt{15}i$$

The equation is now solved.

$$r=2400\sqrt{15}i r=-2400\sqrt{15}i$$