다음을 풀어보세요: 50*10^{3}=(9*10^9)(80*10^66)(-6*10^-6)/r^2

$$50 \times 10 ^ { 3 } = \frac { ( 9 \times 10 ^ { 9 } ) ( 80 \times 10 ^ { 66 } ) ( - 6 \times 10 ^ { - 6 } ) } { r ^ { 2 } }$$

r에 대한 해

$$r=-2400000000000000000000000000000000\sqrt{15}i\approx -0-9.295160031 \cdot 10^{33}i$$

$$r=2400000000000000000000000000000000\sqrt{15}i\approx 9.295160031 \cdot 10^{33}i$$

제곱근 찾기를 사용한 단계

0으로 나누기가 정의되지 않았으므로 r 변수는 0과(와) 같을 수 없습니다. 수식의 양쪽 모두에 r^{2}을(를) 곱합니다.

$$50\times 10^{3}r^{2}=9\times 10^{9}\times 80\times 10^{66}\left(-6\right)\times 10^{-6}$$

같은 기수의 제곱을 곱하려면 해당 지수를 더합니다. 9과(와) 66을(를) 더하여 75을(를) 구합니다.

$$50\times 10^{3}r^{2}=9\times 10^{75}\times 80\left(-6\right)\times 10^{-6}$$

같은 기수의 제곱을 곱하려면 해당 지수를 더합니다. 75과(와) -6을(를) 더하여 69을(를) 구합니다.

$$50\times 10^{3}r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

10의 3제곱을 계산하여 1000을(를) 구합니다.

$$50\times 1000r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

50과(와) 1000을(를) 곱하여 50000(을)를 구합니다.

$$50000r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

10의 69제곱을 계산하여 1000000000000000000000000000000000000000000000000000000000000000000000을(를) 구합니다.

$$50000r^{2}=9\times 1000000000000000000000000000000000000000000000000000000000000000000000\times 80\left(-6\right)$$

9과(와) 1000000000000000000000000000000000000000000000000000000000000000000000을(를) 곱하여 9000000000000000000000000000000000000000000000000000000000000000000000(을)를 구합니다.

$$50000r^{2}=9000000000000000000000000000000000000000000000000000000000000000000000\times 80\left(-6\right)$$

9000000000000000000000000000000000000000000000000000000000000000000000과(와) 80을(를) 곱하여 720000000000000000000000000000000000000000000000000000000000000000000000(을)를 구합니다.

$$50000r^{2}=720000000000000000000000000000000000000000000000000000000000000000000000\left(-6\right)$$

720000000000000000000000000000000000000000000000000000000000000000000000과(와) -6을(를) 곱하여 -4320000000000000000000000000000000000000000000000000000000000000000000000(을)를 구합니다.

$$50000r^{2}=-4320000000000000000000000000000000000000000000000000000000000000000000000$$

양쪽을 50000(으)로 나눕니다.

$$r^{2}=\frac{-4320000000000000000000000000000000000000000000000000000000000000000000000}{50000}$$

-4320000000000000000000000000000000000000000000000000000000000000000000000을(를) 50000(으)로 나눠서 -86400000000000000000000000000000000000000000000000000000000000000000을(를) 구합니다.

$$r^{2}=-86400000000000000000000000000000000000000000000000000000000000000000$$

수식이 이제 해결되었습니다.

$$r=2400000000000000000000000000000000\sqrt{15}i r=-2400000000000000000000000000000000\sqrt{15}i$$

근의 공식을 사용한 단계

0으로 나누기가 정의되지 않았으므로 r 변수는 0과(와) 같을 수 없습니다. 수식의 양쪽 모두에 r^{2}을(를) 곱합니다.

$$50\times 10^{3}r^{2}=9\times 10^{9}\times 80\times 10^{66}\left(-6\right)\times 10^{-6}$$

같은 기수의 제곱을 곱하려면 해당 지수를 더합니다. 9과(와) 66을(를) 더하여 75을(를) 구합니다.

$$50\times 10^{3}r^{2}=9\times 10^{75}\times 80\left(-6\right)\times 10^{-6}$$

같은 기수의 제곱을 곱하려면 해당 지수를 더합니다. 75과(와) -6을(를) 더하여 69을(를) 구합니다.

$$50\times 10^{3}r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

10의 3제곱을 계산하여 1000을(를) 구합니다.

$$50\times 1000r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

50과(와) 1000을(를) 곱하여 50000(을)를 구합니다.

$$50000r^{2}=9\times 10^{69}\times 80\left(-6\right)$$

10의 69제곱을 계산하여 1000000000000000000000000000000000000000000000000000000000000000000000을(를) 구합니다.

$$50000r^{2}=9\times 1000000000000000000000000000000000000000000000000000000000000000000000\times 80\left(-6\right)$$

9과(와) 1000000000000000000000000000000000000000000000000000000000000000000000을(를) 곱하여 9000000000000000000000000000000000000000000000000000000000000000000000(을)를 구합니다.

$$50000r^{2}=9000000000000000000000000000000000000000000000000000000000000000000000\times 80\left(-6\right)$$

9000000000000000000000000000000000000000000000000000000000000000000000과(와) 80을(를) 곱하여 720000000000000000000000000000000000000000000000000000000000000000000000(을)를 구합니다.

$$50000r^{2}=720000000000000000000000000000000000000000000000000000000000000000000000\left(-6\right)$$

720000000000000000000000000000000000000000000000000000000000000000000000과(와) -6을(를) 곱하여 -4320000000000000000000000000000000000000000000000000000000000000000000000(을)를 구합니다.

$$50000r^{2}=-4320000000000000000000000000000000000000000000000000000000000000000000000$$

양쪽에 4320000000000000000000000000000000000000000000000000000000000000000000000을(를) 더합니다.

$$50000r^{2}+4320000000000000000000000000000000000000000000000000000000000000000000000=0$$

이 수식은 표준 형식 ax^{2}+bx+c=0입니다. 근의 공식 \frac{-b±\sqrt{b^{2}-4ac}}{2a}에서 50000을(를) a로, 0을(를) b로, 4320000000000000000000000000000000000000000000000000000000000000000000000을(를) c로 치환합니다.

$$r=\frac{0±\sqrt{0^{2}-4\times 50000\times 4320000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 50000}$$

0을(를) 제곱합니다.

$$r=\frac{0±\sqrt{-4\times 50000\times 4320000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 50000}$$

-4에 50000을(를) 곱합니다.

$$r=\frac{0±\sqrt{-200000\times 4320000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 50000}$$

-200000에 4320000000000000000000000000000000000000000000000000000000000000000000000을(를) 곱합니다.

$$r=\frac{0±\sqrt{-864000000000000000000000000000000000000000000000000000000000000000000000000000}}{2\times 50000}$$

-864000000000000000000000000000000000000000000000000000000000000000000000000000의 제곱근을 구합니다.

$$r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{2\times 50000}$$

2에 50000을(를) 곱합니다.

$$r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000}$$

±이(가) 플러스일 때 수식 r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000}을(를) 풉니다.

$$r=2400000000000000000000000000000000\sqrt{15}i$$

±이(가) 마이너스일 때 수식 r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000}을(를) 풉니다.

$$r=-2400000000000000000000000000000000\sqrt{15}i$$

수식이 이제 해결되었습니다.

$$r=2400000000000000000000000000000000\sqrt{15}i r=-2400000000000000000000000000000000\sqrt{15}i$$