Whakaoti i te 24*10^8=039+x/(027-x)(043-x)

$$24 \times { 10 }^{ 8 } = \frac{ 039+x }{ (027-x)(043-x) }$$

Whakaoti mō x

$$x=\frac{1}{2400000000}\approx 4.166666667 \cdot 10^{-10}$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x^{2}.

$$24\times 10^{8}x^{2}=0\times 39+x$$

Tātaihia te 10 mā te pū o 8, kia riro ko 100000000.

$$24\times 100000000x^{2}=0\times 39+x$$

Whakareatia te 24 ki te 100000000, ka 2400000000.

$$2400000000x^{2}=0\times 39+x$$

Whakareatia te 0 ki te 39, ka 0.

$$2400000000x^{2}=0+x$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$2400000000x^{2}=x$$

Tangohia te x mai i ngā taha e rua.

$$2400000000x^{2}-x=0$$

Tauwehea te x.

$$x\left(2400000000x-1\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 2400000000x-1=0.

$$x=0 x=\frac{1}{2400000000}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{1}{2400000000}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x^{2}.

$$24\times 10^{8}x^{2}=0\times 39+x$$

Tātaihia te 10 mā te pū o 8, kia riro ko 100000000.

$$24\times 100000000x^{2}=0\times 39+x$$

Whakareatia te 24 ki te 100000000, ka 2400000000.

$$2400000000x^{2}=0\times 39+x$$

Whakareatia te 0 ki te 39, ka 0.

$$2400000000x^{2}=0+x$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$2400000000x^{2}=x$$

Tangohia te x mai i ngā taha e rua.

$$2400000000x^{2}-x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2400000000 mō a, -1 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1}}{2\times 2400000000}$$

Tuhia te pūtakerua o te 1.

$$x=\frac{-\left(-1\right)±1}{2\times 2400000000}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±1}{2\times 2400000000}$$

Whakareatia 2 ki te 2400000000.

$$x=\frac{1±1}{4800000000}$$

Nā, me whakaoti te whārite x=\frac{1±1}{4800000000} ina he tāpiri te ±. Tāpiri 1 ki te 1.

$$x=\frac{2}{4800000000}$$

Whakahekea te hautanga \frac{2}{4800000000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{1}{2400000000}$$

Nā, me whakaoti te whārite x=\frac{1±1}{4800000000} ina he tango te ±. Tango 1 mai i 1.

$$x=\frac{0}{4800000000}$$

Whakawehe 0 ki te 4800000000.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{2400000000} x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{1}{2400000000}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x^{2}.

$$24\times 10^{8}x^{2}=0\times 39+x$$

Tātaihia te 10 mā te pū o 8, kia riro ko 100000000.

$$24\times 100000000x^{2}=0\times 39+x$$

Whakareatia te 24 ki te 100000000, ka 2400000000.

$$2400000000x^{2}=0\times 39+x$$

Whakareatia te 0 ki te 39, ka 0.

$$2400000000x^{2}=0+x$$

Ko te tau i tāpiria he kore ka hua koia tonu.

$$2400000000x^{2}=x$$

Tangohia te x mai i ngā taha e rua.

$$2400000000x^{2}-x=0$$

Whakawehea ngā taha e rua ki te 2400000000.

$$\frac{2400000000x^{2}-x}{2400000000}=\frac{0}{2400000000}$$

Mā te whakawehe ki te 2400000000 ka wetekia te whakareanga ki te 2400000000.

$$x^{2}-\frac{1}{2400000000}x=\frac{0}{2400000000}$$

Whakawehe 0 ki te 2400000000.

$$x^{2}-\frac{1}{2400000000}x=0$$

Whakawehea te -\frac{1}{2400000000}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{4800000000}. Nā, tāpiria te pūrua o te -\frac{1}{4800000000} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{2400000000}x+\left(-\frac{1}{4800000000}\right)^{2}=\left(-\frac{1}{4800000000}\right)^{2}$$

Pūruatia -\frac{1}{4800000000} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{2400000000}x+\frac{1}{23040000000000000000}=\frac{1}{23040000000000000000}$$

Tauwehea x^{2}-\frac{1}{2400000000}x+\frac{1}{23040000000000000000}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{4800000000}\right)^{2}=\frac{1}{23040000000000000000}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x-\frac{1}{4800000000}\right)^{2}}=\sqrt{\frac{1}{23040000000000000000}}$$

Whakarūnātia.

$$x-\frac{1}{4800000000}=\frac{1}{4800000000} x-\frac{1}{4800000000}=-\frac{1}{4800000000}$$

Me tāpiri \frac{1}{4800000000} ki ngā taha e rua o te whārite.

$$x=\frac{1}{2400000000} x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{1}{2400000000}$$