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

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

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

Vejledning i at finde kvadratrod

Variablen r må ikke være lig med 0, fordi division med nul ikke er defineret. Multiplicer begge sider af ligningen med r^{2}.

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

Hvis du vil gange potenser for den samme base, skal du tilføje deres eksponenter. Tilføj 9 og 66 for at få 75.

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

Hvis du vil gange potenser for den samme base, skal du tilføje deres eksponenter. Tilføj 75 og -6 for at få 69.

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

Beregn 10 til potensen af 3, og få 1000.

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

Multiplicer 50 og 1000 for at få 50000.

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

Beregn 10 til potensen af 69, og få 1000000000000000000000000000000000000000000000000000000000000000000000.

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

Multiplicer 9 og 1000000000000000000000000000000000000000000000000000000000000000000000 for at få 9000000000000000000000000000000000000000000000000000000000000000000000.

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

Multiplicer 9000000000000000000000000000000000000000000000000000000000000000000000 og 80 for at få 720000000000000000000000000000000000000000000000000000000000000000000000.

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

Multiplicer 720000000000000000000000000000000000000000000000000000000000000000000000 og -6 for at få -4320000000000000000000000000000000000000000000000000000000000000000000000.

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

Divider begge sider med 50000.

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

Divider -4320000000000000000000000000000000000000000000000000000000000000000000000 med 50000 for at få -86400000000000000000000000000000000000000000000000000000000000000000.

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

Ligningen er nu løst.

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

Vejledning i brug af den kvadratiske formel

Variablen r må ikke være lig med 0, fordi division med nul ikke er defineret. Multiplicer begge sider af ligningen med r^{2}.

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

Hvis du vil gange potenser for den samme base, skal du tilføje deres eksponenter. Tilføj 9 og 66 for at få 75.

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

Hvis du vil gange potenser for den samme base, skal du tilføje deres eksponenter. Tilføj 75 og -6 for at få 69.

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

Beregn 10 til potensen af 3, og få 1000.

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

Multiplicer 50 og 1000 for at få 50000.

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

Beregn 10 til potensen af 69, og få 1000000000000000000000000000000000000000000000000000000000000000000000.

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

Multiplicer 9 og 1000000000000000000000000000000000000000000000000000000000000000000000 for at få 9000000000000000000000000000000000000000000000000000000000000000000000.

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

Multiplicer 9000000000000000000000000000000000000000000000000000000000000000000000 og 80 for at få 720000000000000000000000000000000000000000000000000000000000000000000000.

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

Multiplicer 720000000000000000000000000000000000000000000000000000000000000000000000 og -6 for at få -4320000000000000000000000000000000000000000000000000000000000000000000000.

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

Tilføj 4320000000000000000000000000000000000000000000000000000000000000000000000 på begge sider.

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

Denne ligning er i standardform: ax^{2}+bx+c=0. Erstat 50000 med a, 0 med b og 4320000000000000000000000000000000000000000000000000000000000000000000000 med c i den kvadratiske formel \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Kvadrér 0.

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

Multiplicer -4 gange 50000.

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

Multiplicer -200000 gange 4320000000000000000000000000000000000000000000000000000000000000000000000.

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

Tag kvadratroden af -864000000000000000000000000000000000000000000000000000000000000000000000000000.

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

Multiplicer 2 gange 50000.

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

Nu skal du løse ligningen, r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000} når ± er plus.

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

Nu skal du løse ligningen, r=\frac{0±240000000000000000000000000000000000000\sqrt{15}i}{100000} når ± er minus.

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

Ligningen er nu løst.

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