Whakaoti i te 15*10^-5=(x)(x)/1-x

$$15 \times 10 ^ { - 5 } = \frac { ( x ) ( x ) } { 1 - x }$$

Whakaoti mō x

$$x=\frac{\sqrt{240009}-3}{40000}\approx 0.012172678$$

$$x=\frac{-\sqrt{240009}-3}{40000}\approx -0.012322678$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+1.

$$15\times 10^{-5}\left(-x+1\right)=xx$$

Whakareatia te x ki te x, ka x^{2}.

$$15\times 10^{-5}\left(-x+1\right)=x^{2}$$

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

$$15\times \frac{1}{100000}\left(-x+1\right)=x^{2}$$

Whakareatia te 15 ki te \frac{1}{100000}, ka \frac{3}{20000}.

$$\frac{3}{20000}\left(-x+1\right)=x^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{20000} ki te -x+1.

$$-\frac{3}{20000}x+\frac{3}{20000}=x^{2}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$-\frac{3}{20000}x+\frac{3}{20000}-x^{2}=0$$

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.

$$-x^{2}-\frac{3}{20000}x+\frac{3}{20000}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, -\frac{3}{20000} mō b, me \frac{3}{20000} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{3}{20000}\right)±\sqrt{\left(-\frac{3}{20000}\right)^{2}-4\left(-1\right)\times \frac{3}{20000}}}{2\left(-1\right)}$$

Pūruatia -\frac{3}{20000} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-\frac{3}{20000}\right)±\sqrt{\frac{9}{400000000}-4\left(-1\right)\times \frac{3}{20000}}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-\frac{3}{20000}\right)±\sqrt{\frac{9}{400000000}+4\times \frac{3}{20000}}}{2\left(-1\right)}$$

Whakareatia 4 ki te \frac{3}{20000}.

$$x=\frac{-\left(-\frac{3}{20000}\right)±\sqrt{\frac{9}{400000000}+\frac{3}{5000}}}{2\left(-1\right)}$$

Tāpiri \frac{9}{400000000} ki te \frac{3}{5000} 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.

$$x=\frac{-\left(-\frac{3}{20000}\right)±\sqrt{\frac{240009}{400000000}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te \frac{240009}{400000000}.

$$x=\frac{-\left(-\frac{3}{20000}\right)±\frac{\sqrt{240009}}{20000}}{2\left(-1\right)}$$

Ko te tauaro o -\frac{3}{20000} ko \frac{3}{20000}.

$$x=\frac{\frac{3}{20000}±\frac{\sqrt{240009}}{20000}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{\frac{3}{20000}±\frac{\sqrt{240009}}{20000}}{-2}$$

Nā, me whakaoti te whārite x=\frac{\frac{3}{20000}±\frac{\sqrt{240009}}{20000}}{-2} ina he tāpiri te ±. Tāpiri \frac{3}{20000} ki te \frac{\sqrt{240009}}{20000}.

$$x=\frac{\sqrt{240009}+3}{-2\times 20000}$$

Whakawehe \frac{3+\sqrt{240009}}{20000} ki te -2.

$$x=\frac{-\sqrt{240009}-3}{40000}$$

Nā, me whakaoti te whārite x=\frac{\frac{3}{20000}±\frac{\sqrt{240009}}{20000}}{-2} ina he tango te ±. Tango \frac{\sqrt{240009}}{20000} mai i \frac{3}{20000}.

$$x=\frac{3-\sqrt{240009}}{-2\times 20000}$$

Whakawehe \frac{3-\sqrt{240009}}{20000} ki te -2.

$$x=\frac{\sqrt{240009}-3}{40000}$$

Kua oti te whārite te whakatau.

$$x=\frac{-\sqrt{240009}-3}{40000} x=\frac{\sqrt{240009}-3}{40000}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+1.

$$15\times 10^{-5}\left(-x+1\right)=xx$$

Whakareatia te x ki te x, ka x^{2}.

$$15\times 10^{-5}\left(-x+1\right)=x^{2}$$

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

$$15\times \frac{1}{100000}\left(-x+1\right)=x^{2}$$

Whakareatia te 15 ki te \frac{1}{100000}, ka \frac{3}{20000}.

$$\frac{3}{20000}\left(-x+1\right)=x^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{20000} ki te -x+1.

$$-\frac{3}{20000}x+\frac{3}{20000}=x^{2}$$

Tangohia te x^{2} mai i ngā taha e rua.

$$-\frac{3}{20000}x+\frac{3}{20000}-x^{2}=0$$

Tangohia te \frac{3}{20000} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-\frac{3}{20000}x-x^{2}=-\frac{3}{20000}$$

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.

$$-x^{2}-\frac{3}{20000}x=-\frac{3}{20000}$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-\frac{3}{20000}x}{-1}=-\frac{\frac{3}{20000}}{-1}$$

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

$$x^{2}+\left(-\frac{\frac{3}{20000}}{-1}\right)x=-\frac{\frac{3}{20000}}{-1}$$

Whakawehe -\frac{3}{20000} ki te -1.

$$x^{2}+\frac{3}{20000}x=-\frac{\frac{3}{20000}}{-1}$$

Whakawehe -\frac{3}{20000} ki te -1.

$$x^{2}+\frac{3}{20000}x=\frac{3}{20000}$$

Whakawehea te \frac{3}{20000}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{40000}. Nā, tāpiria te pūrua o te \frac{3}{40000} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{3}{20000}x+\left(\frac{3}{40000}\right)^{2}=\frac{3}{20000}+\left(\frac{3}{40000}\right)^{2}$$

Pūruatia \frac{3}{40000} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{3}{20000}x+\frac{9}{1600000000}=\frac{3}{20000}+\frac{9}{1600000000}$$

Tāpiri \frac{3}{20000} ki te \frac{9}{1600000000} 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.

$$x^{2}+\frac{3}{20000}x+\frac{9}{1600000000}=\frac{240009}{1600000000}$$

Tauwehea x^{2}+\frac{3}{20000}x+\frac{9}{1600000000}. 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}.

$$\left(x+\frac{3}{40000}\right)^{2}=\frac{240009}{1600000000}$$

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

$$\sqrt{\left(x+\frac{3}{40000}\right)^{2}}=\sqrt{\frac{240009}{1600000000}}$$

Whakarūnātia.

$$x+\frac{3}{40000}=\frac{\sqrt{240009}}{40000} x+\frac{3}{40000}=-\frac{\sqrt{240009}}{40000}$$

Me tango \frac{3}{40000} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{240009}-3}{40000} x=\frac{-\sqrt{240009}-3}{40000}$$