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

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

Løs for r

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

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

Trinnene ved å finne kvadratroten

Variabelen r kan ikke være lik 0 siden divisjon med null ikke er definert. Multipliser begge sider av ligningen med r^{2}.

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

For å multiplisere potensene av det samme grunntallet, må du legge til eksponentene deres. Legg til 9 og 66 for å få 75.

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

For å multiplisere potensene av det samme grunntallet, må du legge til eksponentene deres. Legg til 75 og -6 for å få 69.

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

Regn ut 10 opphøyd i 3 og få 1000.

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

Multipliser 50 med 1000 for å få 50000.

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

Regn ut 10 opphøyd i 69 og få 1000000000000000000000000000000000000000000000000000000000000000000000.

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

Multipliser 9 med 1000000000000000000000000000000000000000000000000000000000000000000000 for å få 9000000000000000000000000000000000000000000000000000000000000000000000.

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

Multipliser 9000000000000000000000000000000000000000000000000000000000000000000000 med 80 for å få 720000000000000000000000000000000000000000000000000000000000000000000000.

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

Multipliser 720000000000000000000000000000000000000000000000000000000000000000000000 med -6 for å få -4320000000000000000000000000000000000000000000000000000000000000000000000.

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

Del begge sidene på 50000.

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

Del -4320000000000000000000000000000000000000000000000000000000000000000000000 på 50000 for å få -86400000000000000000000000000000000000000000000000000000000000000000.

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

Ligningen er nå løst.

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

Fremgangsmåten ved bruk av andregradsformelen

Variabelen r kan ikke være lik 0 siden divisjon med null ikke er definert. Multipliser begge sider av ligningen med r^{2}.

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

For å multiplisere potensene av det samme grunntallet, må du legge til eksponentene deres. Legg til 9 og 66 for å få 75.

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

For å multiplisere potensene av det samme grunntallet, må du legge til eksponentene deres. Legg til 75 og -6 for å få 69.

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

Regn ut 10 opphøyd i 3 og få 1000.

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

Multipliser 50 med 1000 for å få 50000.

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

Regn ut 10 opphøyd i 69 og få 1000000000000000000000000000000000000000000000000000000000000000000000.

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

Multipliser 9 med 1000000000000000000000000000000000000000000000000000000000000000000000 for å få 9000000000000000000000000000000000000000000000000000000000000000000000.

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

Multipliser 9000000000000000000000000000000000000000000000000000000000000000000000 med 80 for å få 720000000000000000000000000000000000000000000000000000000000000000000000.

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

Multipliser 720000000000000000000000000000000000000000000000000000000000000000000000 med -6 for å få -4320000000000000000000000000000000000000000000000000000000000000000000000.

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

Legg til 4320000000000000000000000000000000000000000000000000000000000000000000000 på begge sider.

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

Denne ligningen er i standard form: ax^{2}+bx+c=0. Sett inn 50000 for a, 0 for b og 4320000000000000000000000000000000000000000000000000000000000000000000000 for c i andregradsformelen, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Kvadrer 0.

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

Multipliser -4 ganger 50000.

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

Multipliser -200000 ganger 4320000000000000000000000000000000000000000000000000000000000000000000000.

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

Ta kvadratroten av -864000000000000000000000000000000000000000000000000000000000000000000000000000.

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

Multipliser 2 ganger 50000.

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

Nå kan du løse formelen r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000} når ± er pluss.

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

Nå kan du løse formelen r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000} når ± er minus.

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

Ligningen er nå løst.

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