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

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

Riješite za r

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

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

Koraci pronalaženjem kvadratnog korijena

Promjenjiva r ne može biti jednaka vrijednosti 0 zato što dijeljenje nulom nije definirano. Pomnožite obje strane jednačine sa r^{2}.

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

Da biste pomnožili stepene iste osnove, saberite eksponente. Saberite 9 i 66 da biste dobili 75.

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

Da biste pomnožili stepene iste osnove, saberite eksponente. Saberite 75 i -6 da biste dobili 69.

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

Izračunajte 10 stepen od 3 i dobijte 1000.

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

Pomnožite 50 i 1000 da biste dobili 50000.

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

Izračunajte 10 stepen od 69 i dobijte 1000000000000000000000000000000000000000000000000000000000000000000000.

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

Pomnožite 9 i 1000000000000000000000000000000000000000000000000000000000000000000000 da biste dobili 9000000000000000000000000000000000000000000000000000000000000000000000.

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

Pomnožite 9000000000000000000000000000000000000000000000000000000000000000000000 i 80 da biste dobili 720000000000000000000000000000000000000000000000000000000000000000000000.

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

Pomnožite 720000000000000000000000000000000000000000000000000000000000000000000000 i -6 da biste dobili -4320000000000000000000000000000000000000000000000000000000000000000000000.

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

Podijelite obje strane s 50000.

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

Podijelite -4320000000000000000000000000000000000000000000000000000000000000000000000 sa 50000 da biste dobili -86400000000000000000000000000000000000000000000000000000000000000000.

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

Jednačina je riješena.

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

Koraci pomoću kvadratne formule

Promjenjiva r ne može biti jednaka vrijednosti 0 zato što dijeljenje nulom nije definirano. Pomnožite obje strane jednačine sa r^{2}.

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

Da biste pomnožili stepene iste osnove, saberite eksponente. Saberite 9 i 66 da biste dobili 75.

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

Da biste pomnožili stepene iste osnove, saberite eksponente. Saberite 75 i -6 da biste dobili 69.

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

Izračunajte 10 stepen od 3 i dobijte 1000.

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

Pomnožite 50 i 1000 da biste dobili 50000.

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

Izračunajte 10 stepen od 69 i dobijte 1000000000000000000000000000000000000000000000000000000000000000000000.

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

Pomnožite 9 i 1000000000000000000000000000000000000000000000000000000000000000000000 da biste dobili 9000000000000000000000000000000000000000000000000000000000000000000000.

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

Pomnožite 9000000000000000000000000000000000000000000000000000000000000000000000 i 80 da biste dobili 720000000000000000000000000000000000000000000000000000000000000000000000.

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

Pomnožite 720000000000000000000000000000000000000000000000000000000000000000000000 i -6 da biste dobili -4320000000000000000000000000000000000000000000000000000000000000000000000.

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

Dodajte 4320000000000000000000000000000000000000000000000000000000000000000000000 na obje strane.

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

Ova jednačina je u standardnom obliku: ax^{2}+bx+c=0. Zamijenite 50000 i a, 0 i b, kao i 4320000000000000000000000000000000000000000000000000000000000000000000000 i c u kvadratnoj formuli, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Izračunajte kvadrat od 0.

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

Pomnožite -4 i 50000.

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

Pomnožite -200000 i 4320000000000000000000000000000000000000000000000000000000000000000000000.

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

Izračunajte kvadratni korijen od -864000000000000000000000000000000000000000000000000000000000000000000000000000.

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

Pomnožite 2 i 50000.

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

Sada riješite jednačinu r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000} kada je ± plus.

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

Sada riješite jednačinu r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000} kada je ± minus.

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

Jednačina je riješena.

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