Whakaoti i te 174*10^-5=x^2/01-x

$$174 \times { 10 }^{ -5 } = \frac{ { x }^{ 2 } }{ 01-x }$$

Whakaoti mō x

$$x=-\frac{87}{50000}=-0.00174$$

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.

$$174\times 10^{-5}x=-x^{2}$$

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

$$174\times \frac{1}{100000}x=-x^{2}$$

Whakareatia te 174 ki te \frac{1}{100000}, ka \frac{87}{50000}.

$$\frac{87}{50000}x=-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$\frac{87}{50000}x+x^{2}=0$$

Tauwehea te x.

$$x\left(\frac{87}{50000}+x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te \frac{87}{50000}+x=0.

$$x=0 x=-\frac{87}{50000}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{87}{50000}$$

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.

$$174\times 10^{-5}x=-x^{2}$$

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

$$174\times \frac{1}{100000}x=-x^{2}$$

Whakareatia te 174 ki te \frac{1}{100000}, ka \frac{87}{50000}.

$$\frac{87}{50000}x=-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$\frac{87}{50000}x+x^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$x^{2}+\frac{87}{50000}x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, \frac{87}{50000} mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{87}{50000}±\sqrt{\left(\frac{87}{50000}\right)^{2}}}{2}$$

Tuhia te pūtakerua o te \left(\frac{87}{50000}\right)^{2}.

$$x=\frac{-\frac{87}{50000}±\frac{87}{50000}}{2}$$

Nā, me whakaoti te whārite x=\frac{-\frac{87}{50000}±\frac{87}{50000}}{2} ina he tāpiri te ±. Tāpiri -\frac{87}{50000} ki te \frac{87}{50000} 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.

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

Whakawehe 0 ki te 2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-\frac{87}{50000}±\frac{87}{50000}}{2} ina he tango te ±. Tango \frac{87}{50000} mai i -\frac{87}{50000} 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.

$$x=-\frac{\frac{87}{25000}}{2}$$

Whakawehe -\frac{87}{25000} ki te 2.

$$x=-\frac{87}{50000}$$

Kua oti te whārite te whakatau.

$$x=0 x=-\frac{87}{50000}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{87}{50000}$$

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.

$$174\times 10^{-5}x=-x^{2}$$

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

$$174\times \frac{1}{100000}x=-x^{2}$$

Whakareatia te 174 ki te \frac{1}{100000}, ka \frac{87}{50000}.

$$\frac{87}{50000}x=-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$\frac{87}{50000}x+x^{2}=0$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$x^{2}+\frac{87}{50000}x=0$$

Whakawehea te \frac{87}{50000}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{87}{100000}. Nā, tāpiria te pūrua o te \frac{87}{100000} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{87}{50000}x+\left(\frac{87}{100000}\right)^{2}=\left(\frac{87}{100000}\right)^{2}$$

Pūruatia \frac{87}{100000} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{87}{50000}x+\frac{7569}{10000000000}=\frac{7569}{10000000000}$$

Tauwehea x^{2}+\frac{87}{50000}x+\frac{7569}{10000000000}. 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}.

$$\left(x+\frac{87}{100000}\right)^{2}=\frac{7569}{10000000000}$$

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

$$\sqrt{\left(x+\frac{87}{100000}\right)^{2}}=\sqrt{\frac{7569}{10000000000}}$$

Whakarūnātia.

$$x+\frac{87}{100000}=\frac{87}{100000} x+\frac{87}{100000}=-\frac{87}{100000}$$

Me tango \frac{87}{100000} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{87}{50000}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=-\frac{87}{50000}$$