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

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

Реши за r

$$r=-2400000000000000000000000000000000\sqrt{15}i\approx -0-9,295160031 \cdot 10^{33}i$$

$$r=2400000000000000000000000000000000\sqrt{15}i\approx 9,295160031 \cdot 10^{33}i$$

Чекори за наоѓање квадратен корен

Променливата r не може да биде еднаква на 0 бидејќи делењето со нула не е дефинирано. Помножете ги двете страни на равенката со r^{2}.

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

За да множите степени со иста основа, соберете ги нивните степенови показатели. Соберете ги 9 и 66 за да добиете 75.

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

За да множите степени со иста основа, соберете ги нивните степенови показатели. Соберете ги 75 и -6 за да добиете 69.

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

Пресметајте колку е 10 на степен од 3 и добијте 1000.

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

Помножете 50 и 1000 за да добиете 50000.

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

Пресметајте колку е 10 на степен од 69 и добијте 1000000000000000000000000000000000000000000000000000000000000000000000.

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

Помножете 9 и 1000000000000000000000000000000000000000000000000000000000000000000000 за да добиете 9000000000000000000000000000000000000000000000000000000000000000000000.

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

Помножете 9000000000000000000000000000000000000000000000000000000000000000000000 и 80 за да добиете 720000000000000000000000000000000000000000000000000000000000000000000000.

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

Помножете 720000000000000000000000000000000000000000000000000000000000000000000000 и -6 за да добиете -4320000000000000000000000000000000000000000000000000000000000000000000000.

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

Поделете ги двете страни со 50000.

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

Поделете -4320000000000000000000000000000000000000000000000000000000000000000000000 со 50000 за да добиете -86400000000000000000000000000000000000000000000000000000000000000000.

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

Равенката сега е решена.

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

Чекори за користење на формулата за квадратна равенка

Променливата r не може да биде еднаква на 0 бидејќи делењето со нула не е дефинирано. Помножете ги двете страни на равенката со r^{2}.

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

За да множите степени со иста основа, соберете ги нивните степенови показатели. Соберете ги 9 и 66 за да добиете 75.

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

За да множите степени со иста основа, соберете ги нивните степенови показатели. Соберете ги 75 и -6 за да добиете 69.

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

Пресметајте колку е 10 на степен од 3 и добијте 1000.

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

Помножете 50 и 1000 за да добиете 50000.

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

Пресметајте колку е 10 на степен од 69 и добијте 1000000000000000000000000000000000000000000000000000000000000000000000.

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

Помножете 9 и 1000000000000000000000000000000000000000000000000000000000000000000000 за да добиете 9000000000000000000000000000000000000000000000000000000000000000000000.

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

Помножете 9000000000000000000000000000000000000000000000000000000000000000000000 и 80 за да добиете 720000000000000000000000000000000000000000000000000000000000000000000000.

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

Помножете 720000000000000000000000000000000000000000000000000000000000000000000000 и -6 за да добиете -4320000000000000000000000000000000000000000000000000000000000000000000000.

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

Додај 4320000000000000000000000000000000000000000000000000000000000000000000000 на двете страни.

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

Оваа равенка е во стандардна форма: ax^{2}+bx+c=0. Ставете 50000 за a, 0 за b и 4320000000000000000000000000000000000000000000000000000000000000000000000 за c во формулата за квадратна равенка \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Квадрат од 0.

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

Множење на -4 со 50000.

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

Множење на -200000 со 4320000000000000000000000000000000000000000000000000000000000000000000000.

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

Вадење квадратен корен од -864000000000000000000000000000000000000000000000000000000000000000000000000000.

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

Множење на 2 со 50000.

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

Сега решете ја равенката r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000} кога ± ќе биде плус.

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

Сега решете ја равенката r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000} кога ± ќе биде минус.

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

Равенката сега е решена.

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