Whakaoti i te 463*10^-3(0123-x)=x^2

$$463 \times 10 ^ { - 3 } ( 0123 - x ) = x ^ { 2 }$$

Whakaoti mō x

$$x=-\frac{463}{1000}=-0.463$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tātaihia te 10 mā te pū o -3, kia riro ko \frac{1}{1000}.

$$463\times \frac{1}{1000}\left(0\times 123-x\right)=x^{2}$$

Whakareatia te 463 ki te \frac{1}{1000}, ka \frac{463}{1000}.

$$\frac{463}{1000}\left(0\times 123-x\right)=x^{2}$$

Whakareatia te 0 ki te 123, ka 0.

$$\frac{463}{1000}\left(0-x\right)=x^{2}$$

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

$$\frac{463}{1000}\left(-1\right)x=x^{2}$$

Whakareatia te \frac{463}{1000} ki te -1, ka -\frac{463}{1000}.

$$-\frac{463}{1000}x=x^{2}$$

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

$$-\frac{463}{1000}x-x^{2}=0$$

Tauwehea te x.

$$x\left(-\frac{463}{1000}-x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -\frac{463}{1000}-x=0.

$$x=0 x=-\frac{463}{1000}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 10 mā te pū o -3, kia riro ko \frac{1}{1000}.

$$463\times \frac{1}{1000}\left(0\times 123-x\right)=x^{2}$$

Whakareatia te 463 ki te \frac{1}{1000}, ka \frac{463}{1000}.

$$\frac{463}{1000}\left(0\times 123-x\right)=x^{2}$$

Whakareatia te 0 ki te 123, ka 0.

$$\frac{463}{1000}\left(0-x\right)=x^{2}$$

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

$$\frac{463}{1000}\left(-1\right)x=x^{2}$$

Whakareatia te \frac{463}{1000} ki te -1, ka -\frac{463}{1000}.

$$-\frac{463}{1000}x=x^{2}$$

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

$$-\frac{463}{1000}x-x^{2}=0$$

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.

$$-x^{2}-\frac{463}{1000}x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, -\frac{463}{1000} mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{463}{1000}\right)±\sqrt{\left(-\frac{463}{1000}\right)^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te \left(-\frac{463}{1000}\right)^{2}.

$$x=\frac{-\left(-\frac{463}{1000}\right)±\frac{463}{1000}}{2\left(-1\right)}$$

Ko te tauaro o -\frac{463}{1000} ko \frac{463}{1000}.

$$x=\frac{\frac{463}{1000}±\frac{463}{1000}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{\frac{463}{1000}±\frac{463}{1000}}{-2}$$

Nā, me whakaoti te whārite x=\frac{\frac{463}{1000}±\frac{463}{1000}}{-2} ina he tāpiri te ±. Tāpiri \frac{463}{1000} ki te \frac{463}{1000} 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.

$$x=\frac{\frac{463}{500}}{-2}$$

Whakawehe \frac{463}{500} ki te -2.

$$x=-\frac{463}{1000}$$

Nā, me whakaoti te whārite x=\frac{\frac{463}{1000}±\frac{463}{1000}}{-2} ina he tango te ±. Tango \frac{463}{1000} mai i \frac{463}{1000} 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.

$$x=-\frac{463}{1000} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tātaihia te 10 mā te pū o -3, kia riro ko \frac{1}{1000}.

$$463\times \frac{1}{1000}\left(0\times 123-x\right)=x^{2}$$

Whakareatia te 463 ki te \frac{1}{1000}, ka \frac{463}{1000}.

$$\frac{463}{1000}\left(0\times 123-x\right)=x^{2}$$

Whakareatia te 0 ki te 123, ka 0.

$$\frac{463}{1000}\left(0-x\right)=x^{2}$$

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

$$\frac{463}{1000}\left(-1\right)x=x^{2}$$

Whakareatia te \frac{463}{1000} ki te -1, ka -\frac{463}{1000}.

$$-\frac{463}{1000}x=x^{2}$$

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

$$-\frac{463}{1000}x-x^{2}=0$$

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.

$$-x^{2}-\frac{463}{1000}x=0$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-\frac{463}{1000}x}{-1}=\frac{0}{-1}$$

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

$$x^{2}+\left(-\frac{\frac{463}{1000}}{-1}\right)x=\frac{0}{-1}$$

Whakawehe -\frac{463}{1000} ki te -1.

$$x^{2}+\frac{463}{1000}x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$x^{2}+\frac{463}{1000}x=0$$

Whakawehea te \frac{463}{1000}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{463}{2000}. Nā, tāpiria te pūrua o te \frac{463}{2000} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{463}{1000}x+\left(\frac{463}{2000}\right)^{2}=\left(\frac{463}{2000}\right)^{2}$$

Pūruatia \frac{463}{2000} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{463}{1000}x+\frac{214369}{4000000}=\frac{214369}{4000000}$$

Tauwehea x^{2}+\frac{463}{1000}x+\frac{214369}{4000000}. 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}.

$$\left(x+\frac{463}{2000}\right)^{2}=\frac{214369}{4000000}$$

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

$$\sqrt{\left(x+\frac{463}{2000}\right)^{2}}=\sqrt{\frac{214369}{4000000}}$$

Whakarūnātia.

$$x+\frac{463}{2000}=\frac{463}{2000} x+\frac{463}{2000}=-\frac{463}{2000}$$

Me tango \frac{463}{2000} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{463}{1000}$$