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5\times 10^{3}r^{2}=9\times 10^{9}\times 8\times 10^{66}\left(-6\right)\times 10^{-6}
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^{75}\times 8\left(-6\right)\times 10^{-6}
To multiply powers of the same base, add their exponents. Add 9 and 66 to get 75.
5\times 10^{3}r^{2}=9\times 10^{69}\times 8\left(-6\right)
To multiply powers of the same base, add their exponents. Add 75 and -6 to get 69.
5\times 1000r^{2}=9\times 10^{69}\times 8\left(-6\right)
Calculate 10 to the power of 3 and get 1000.
5000r^{2}=9\times 10^{69}\times 8\left(-6\right)
Multiply 5 and 1000 to get 5000.
5000r^{2}=9\times 1000000000000000000000000000000000000000000000000000000000000000000000\times 8\left(-6\right)
Calculate 10 to the power of 69 and get 1000000000000000000000000000000000000000000000000000000000000000000000.
5000r^{2}=9000000000000000000000000000000000000000000000000000000000000000000000\times 8\left(-6\right)
Multiply 9 and 1000000000000000000000000000000000000000000000000000000000000000000000 to get 9000000000000000000000000000000000000000000000000000000000000000000000.
5000r^{2}=72000000000000000000000000000000000000000000000000000000000000000000000\left(-6\right)
Multiply 9000000000000000000000000000000000000000000000000000000000000000000000 and 8 to get 72000000000000000000000000000000000000000000000000000000000000000000000.
5000r^{2}=-432000000000000000000000000000000000000000000000000000000000000000000000
Multiply 72000000000000000000000000000000000000000000000000000000000000000000000 and -6 to get -432000000000000000000000000000000000000000000000000000000000000000000000.
r^{2}=\frac{-432000000000000000000000000000000000000000000000000000000000000000000000}{5000}
Divide both sides by 5000.
r^{2}=-86400000000000000000000000000000000000000000000000000000000000000000
Divide -432000000000000000000000000000000000000000000000000000000000000000000000 by 5000 to get -86400000000000000000000000000000000000000000000000000000000000000000.
r=2400000000000000000000000000000000\sqrt{15}i r=-2400000000000000000000000000000000\sqrt{15}i
The equation is now solved.
5\times 10^{3}r^{2}=9\times 10^{9}\times 8\times 10^{66}\left(-6\right)\times 10^{-6}
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^{75}\times 8\left(-6\right)\times 10^{-6}
To multiply powers of the same base, add their exponents. Add 9 and 66 to get 75.
5\times 10^{3}r^{2}=9\times 10^{69}\times 8\left(-6\right)
To multiply powers of the same base, add their exponents. Add 75 and -6 to get 69.
5\times 1000r^{2}=9\times 10^{69}\times 8\left(-6\right)
Calculate 10 to the power of 3 and get 1000.
5000r^{2}=9\times 10^{69}\times 8\left(-6\right)
Multiply 5 and 1000 to get 5000.
5000r^{2}=9\times 1000000000000000000000000000000000000000000000000000000000000000000000\times 8\left(-6\right)
Calculate 10 to the power of 69 and get 1000000000000000000000000000000000000000000000000000000000000000000000.
5000r^{2}=9000000000000000000000000000000000000000000000000000000000000000000000\times 8\left(-6\right)
Multiply 9 and 1000000000000000000000000000000000000000000000000000000000000000000000 to get 9000000000000000000000000000000000000000000000000000000000000000000000.
5000r^{2}=72000000000000000000000000000000000000000000000000000000000000000000000\left(-6\right)
Multiply 9000000000000000000000000000000000000000000000000000000000000000000000 and 8 to get 72000000000000000000000000000000000000000000000000000000000000000000000.
5000r^{2}=-432000000000000000000000000000000000000000000000000000000000000000000000
Multiply 72000000000000000000000000000000000000000000000000000000000000000000000 and -6 to get -432000000000000000000000000000000000000000000000000000000000000000000000.
5000r^{2}+432000000000000000000000000000000000000000000000000000000000000000000000=0
Add 432000000000000000000000000000000000000000000000000000000000000000000000 to both sides.
r=\frac{0±\sqrt{0^{2}-4\times 5000\times 432000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 5000}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 5000 for a, 0 for b, and 432000000000000000000000000000000000000000000000000000000000000000000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
r=\frac{0±\sqrt{-4\times 5000\times 432000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 5000}
Square 0.
r=\frac{0±\sqrt{-20000\times 432000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 5000}
Multiply -4 times 5000.
r=\frac{0±\sqrt{-8640000000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 5000}
Multiply -20000 times 432000000000000000000000000000000000000000000000000000000000000000000000.
r=\frac{0±24000000000000000000000000000000000000\sqrt{15}i}{2\times 5000}
Take the square root of -8640000000000000000000000000000000000000000000000000000000000000000000000000.
r=\frac{0±24000000000000000000000000000000000000\sqrt{15}i}{10000}
Multiply 2 times 5000.
r=2400000000000000000000000000000000\sqrt{15}i
Now solve the equation r=\frac{0±24000000000000000000000000000000000000\sqrt{15}i}{10000} when ± is plus.
r=-2400000000000000000000000000000000\sqrt{15}i
Now solve the equation r=\frac{0±24000000000000000000000000000000000000\sqrt{15}i}{10000} when ± is minus.
r=2400000000000000000000000000000000\sqrt{15}i r=-2400000000000000000000000000000000\sqrt{15}i
The equation is now solved.