Whakaoti i te x^2/035-x=83176*10^-5

$$\frac{ { x }^{ 2 } }{ 035-x } = 83176 \times { 10 }^{ -5 }$$

Whakaoti mō x

$$x=-\frac{10397}{12500}=-0.83176$$

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.

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

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

$$-x^{2}=83176\times \frac{1}{100000}x$$

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

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

Tangohia te \frac{10397}{12500}x mai i ngā taha e rua.

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

Tauwehea te x.

$$x\left(-x-\frac{10397}{12500}\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -x-\frac{10397}{12500}=0.

$$x=0 x=-\frac{10397}{12500}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{10397}{12500}$$

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.

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

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

$$-x^{2}=83176\times \frac{1}{100000}x$$

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

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

Tangohia te \frac{10397}{12500}x mai i ngā taha e rua.

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

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

$$x=\frac{-\left(-\frac{10397}{12500}\right)±\sqrt{\left(-\frac{10397}{12500}\right)^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te \left(-\frac{10397}{12500}\right)^{2}.

$$x=\frac{-\left(-\frac{10397}{12500}\right)±\frac{10397}{12500}}{2\left(-1\right)}$$

Ko te tauaro o -\frac{10397}{12500} ko \frac{10397}{12500}.

$$x=\frac{\frac{10397}{12500}±\frac{10397}{12500}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

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

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

$$x=\frac{\frac{10397}{6250}}{-2}$$

Whakawehe \frac{10397}{6250} ki te -2.

$$x=-\frac{10397}{12500}$$

Nā, me whakaoti te whārite x=\frac{\frac{10397}{12500}±\frac{10397}{12500}}{-2} ina he tango te ±. Tango \frac{10397}{12500} mai i \frac{10397}{12500} mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

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

Whakawehe 0 ki te -2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-\frac{10397}{12500} x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{10397}{12500}$$

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.

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

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

$$-x^{2}=83176\times \frac{1}{100000}x$$

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

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

Tangohia te \frac{10397}{12500}x mai i ngā taha e rua.

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

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-\frac{10397}{12500}x}{-1}=\frac{0}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\left(-\frac{\frac{10397}{12500}}{-1}\right)x=\frac{0}{-1}$$

Whakawehe -\frac{10397}{12500} ki te -1.

$$x^{2}+\frac{10397}{12500}x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

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

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.

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

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

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

Tauwehea x^{2}+\frac{10397}{12500}x+\frac{108097609}{625000000}. 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}.

$$\left(x+\frac{10397}{25000}\right)^{2}=\frac{108097609}{625000000}$$

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

$$\sqrt{\left(x+\frac{10397}{25000}\right)^{2}}=\sqrt{\frac{108097609}{625000000}}$$

Whakarūnātia.

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

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

$$x=0 x=-\frac{10397}{12500}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{10397}{12500}$$