Whakaoti i te x^2/308-x=83176*10^-5

$$\frac{ { x }^{ 2 } }{ 308-x } = 83176 \times { 10 }^{ -5 }$$

Whakaoti mō x

$$x = \frac{\sqrt{160221897609} - 10397}{25000} \approx 15.595211036$$

$$x=\frac{-\sqrt{160221897609}-10397}{25000}\approx -16.426971036$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 308 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+308.

$$x^{2}=83176\times 10^{-5}\left(-x+308\right)$$

Tātaihia te 10 mā te pū o -5, kia riro ko \frac{1}{100000}.

$$x^{2}=83176\times \frac{1}{100000}\left(-x+308\right)$$

Whakareatia te 83176 ki te \frac{1}{100000}, ka \frac{10397}{12500}.

$$x^{2}=\frac{10397}{12500}\left(-x+308\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{10397}{12500} ki te -x+308.

$$x^{2}=-\frac{10397}{12500}x+\frac{800569}{3125}$$

Me tāpiri te \frac{10397}{12500}x ki ngā taha e rua.

$$x^{2}+\frac{10397}{12500}x=\frac{800569}{3125}$$

Tangohia te \frac{800569}{3125} mai i ngā taha e rua.

$$x^{2}+\frac{10397}{12500}x-\frac{800569}{3125}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, \frac{10397}{12500} mō b, me -\frac{800569}{3125} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\left(\frac{10397}{12500}\right)^{2}-4\left(-\frac{800569}{3125}\right)}}{2}$$

Pūruatia \frac{10397}{12500} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\frac{108097609}{156250000}-4\left(-\frac{800569}{3125}\right)}}{2}$$

Whakareatia -4 ki te -\frac{800569}{3125}.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\frac{108097609}{156250000}+\frac{3202276}{3125}}}{2}$$

Tāpiri \frac{108097609}{156250000} ki te \frac{3202276}{3125} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{-\frac{10397}{12500}±\sqrt{\frac{160221897609}{156250000}}}{2}$$

Tuhia te pūtakerua o te \frac{160221897609}{156250000}.

$$x=\frac{-\frac{10397}{12500}±\frac{\sqrt{160221897609}}{12500}}{2}$$

Nā, me whakaoti te whārite x=\frac{-\frac{10397}{12500}±\frac{\sqrt{160221897609}}{12500}}{2} ina he tāpiri te ±. Tāpiri -\frac{10397}{12500} ki te \frac{\sqrt{160221897609}}{12500}.

$$x=\frac{\sqrt{160221897609}-10397}{2\times 12500}$$

Whakawehe \frac{-10397+\sqrt{160221897609}}{12500} ki te 2.

$$x=\frac{\sqrt{160221897609}-10397}{25000}$$

Nā, me whakaoti te whārite x=\frac{-\frac{10397}{12500}±\frac{\sqrt{160221897609}}{12500}}{2} ina he tango te ±. Tango \frac{\sqrt{160221897609}}{12500} mai i -\frac{10397}{12500}.

$$x=\frac{-\sqrt{160221897609}-10397}{2\times 12500}$$

Whakawehe \frac{-10397-\sqrt{160221897609}}{12500} ki te 2.

$$x=\frac{-\sqrt{160221897609}-10397}{25000}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{160221897609}-10397}{25000} x=\frac{-\sqrt{160221897609}-10397}{25000}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 308 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+308.

$$x^{2}=83176\times 10^{-5}\left(-x+308\right)$$

Tātaihia te 10 mā te pū o -5, kia riro ko \frac{1}{100000}.

$$x^{2}=83176\times \frac{1}{100000}\left(-x+308\right)$$

Whakareatia te 83176 ki te \frac{1}{100000}, ka \frac{10397}{12500}.

$$x^{2}=\frac{10397}{12500}\left(-x+308\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{10397}{12500} ki te -x+308.

$$x^{2}=-\frac{10397}{12500}x+\frac{800569}{3125}$$

Me tāpiri te \frac{10397}{12500}x ki ngā taha e rua.

$$x^{2}+\frac{10397}{12500}x=\frac{800569}{3125}$$

Whakawehea te \frac{10397}{12500}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{10397}{25000}. Nā, tāpiria te pūrua o te \frac{10397}{25000} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{10397}{12500}x+\left(\frac{10397}{25000}\right)^{2}=\frac{800569}{3125}+\left(\frac{10397}{25000}\right)^{2}$$

Pūruatia \frac{10397}{25000} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}=\frac{800569}{3125}+\frac{108097609}{625000000}$$

Tāpiri \frac{800569}{3125} ki te \frac{108097609}{625000000} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}=\frac{160221897609}{625000000}$$

Tauwehea te x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{10397}{25000}\right)^{2}=\frac{160221897609}{625000000}$$

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

$$\sqrt{\left(x+\frac{10397}{25000}\right)^{2}}=\sqrt{\frac{160221897609}{625000000}}$$

Whakarūnātia.

$$x+\frac{10397}{25000}=\frac{\sqrt{160221897609}}{25000} x+\frac{10397}{25000}=-\frac{\sqrt{160221897609}}{25000}$$

Me tango \frac{10397}{25000} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{160221897609}-10397}{25000} x=\frac{-\sqrt{160221897609}-10397}{25000}$$