Whakaoti i te left(05268-xright)left(00268-xright)/09732+x=72*10^-4

$$\frac{ \left( 05268-x \right) \left( 00268-x \right) }{ 09732+x } = 72 \times { 10 }^{ -4 }$$

Whakaoti mō x

$$x=\frac{9}{1250}=0.0072$$

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.

$$\left(0\times 5268-x\right)\left(0\times 0\times 268-x\right)=72\times 10^{-4}x$$

Whakareatia te 0 ki te 5268, ka 0.

$$\left(0-x\right)\left(0\times 0\times 268-x\right)=72\times 10^{-4}x$$

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

$$-x\left(0\times 0\times 268-x\right)=72\times 10^{-4}x$$

Whakareatia te 0 ki te 0, ka 0.

$$-x\left(0\times 268-x\right)=72\times 10^{-4}x$$

Whakareatia te 0 ki te 268, ka 0.

$$-x\left(0-x\right)=72\times 10^{-4}x$$

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

$$-x\left(-1\right)x=72\times 10^{-4}x$$

Whakareatia te -1 ki te -1, ka 1.

$$xx=72\times 10^{-4}x$$

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

$$x^{2}=72\times 10^{-4}x$$

Tātaihia te 10 mā te pū o -4, kia riro ko \frac{1}{10000}.

$$x^{2}=72\times \frac{1}{10000}x$$

Whakareatia te 72 ki te \frac{1}{10000}, ka \frac{9}{1250}.

$$x^{2}=\frac{9}{1250}x$$

Tangohia te \frac{9}{1250}x mai i ngā taha e rua.

$$x^{2}-\frac{9}{1250}x=0$$

Tauwehea te x.

$$x\left(x-\frac{9}{1250}\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te x-\frac{9}{1250}=0.

$$x=0 x=\frac{9}{1250}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{9}{1250}$$

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.

$$\left(0\times 5268-x\right)\left(0\times 0\times 268-x\right)=72\times 10^{-4}x$$

Whakareatia te 0 ki te 5268, ka 0.

$$\left(0-x\right)\left(0\times 0\times 268-x\right)=72\times 10^{-4}x$$

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

$$-x\left(0\times 0\times 268-x\right)=72\times 10^{-4}x$$

Whakareatia te 0 ki te 0, ka 0.

$$-x\left(0\times 268-x\right)=72\times 10^{-4}x$$

Whakareatia te 0 ki te 268, ka 0.

$$-x\left(0-x\right)=72\times 10^{-4}x$$

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

$$-x\left(-1\right)x=72\times 10^{-4}x$$

Whakareatia te -1 ki te -1, ka 1.

$$xx=72\times 10^{-4}x$$

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

$$x^{2}=72\times 10^{-4}x$$

Tātaihia te 10 mā te pū o -4, kia riro ko \frac{1}{10000}.

$$x^{2}=72\times \frac{1}{10000}x$$

Whakareatia te 72 ki te \frac{1}{10000}, ka \frac{9}{1250}.

$$x^{2}=\frac{9}{1250}x$$

Tangohia te \frac{9}{1250}x mai i ngā taha e rua.

$$x^{2}-\frac{9}{1250}x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -\frac{9}{1250} mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{9}{1250}\right)±\sqrt{\left(-\frac{9}{1250}\right)^{2}}}{2}$$

Tuhia te pūtakerua o te \left(-\frac{9}{1250}\right)^{2}.

$$x=\frac{-\left(-\frac{9}{1250}\right)±\frac{9}{1250}}{2}$$

Ko te tauaro o -\frac{9}{1250} ko \frac{9}{1250}.

$$x=\frac{\frac{9}{1250}±\frac{9}{1250}}{2}$$

Nā, me whakaoti te whārite x=\frac{\frac{9}{1250}±\frac{9}{1250}}{2} ina he tāpiri te ±. Tāpiri \frac{9}{1250} ki te \frac{9}{1250} 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.

$$x=\frac{\frac{9}{625}}{2}$$

Whakawehe \frac{9}{625} ki te 2.

$$x=\frac{9}{1250}$$

Nā, me whakaoti te whārite x=\frac{\frac{9}{1250}±\frac{9}{1250}}{2} ina he tango te ±. Tango \frac{9}{1250} mai i \frac{9}{1250} 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.

$$x=\frac{9}{1250} x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{9}{1250}$$

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.

$$\left(0\times 5268-x\right)\left(0\times 0\times 268-x\right)=72\times 10^{-4}x$$

Whakareatia te 0 ki te 5268, ka 0.

$$\left(0-x\right)\left(0\times 0\times 268-x\right)=72\times 10^{-4}x$$

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

$$-x\left(0\times 0\times 268-x\right)=72\times 10^{-4}x$$

Whakareatia te 0 ki te 0, ka 0.

$$-x\left(0\times 268-x\right)=72\times 10^{-4}x$$

Whakareatia te 0 ki te 268, ka 0.

$$-x\left(0-x\right)=72\times 10^{-4}x$$

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

$$-x\left(-1\right)x=72\times 10^{-4}x$$

Whakareatia te -1 ki te -1, ka 1.

$$xx=72\times 10^{-4}x$$

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

$$x^{2}=72\times 10^{-4}x$$

Tātaihia te 10 mā te pū o -4, kia riro ko \frac{1}{10000}.

$$x^{2}=72\times \frac{1}{10000}x$$

Whakareatia te 72 ki te \frac{1}{10000}, ka \frac{9}{1250}.

$$x^{2}=\frac{9}{1250}x$$

Tangohia te \frac{9}{1250}x mai i ngā taha e rua.

$$x^{2}-\frac{9}{1250}x=0$$

Whakawehea te -\frac{9}{1250}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{2500}. Nā, tāpiria te pūrua o te -\frac{9}{2500} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{9}{1250}x+\left(-\frac{9}{2500}\right)^{2}=\left(-\frac{9}{2500}\right)^{2}$$

Pūruatia -\frac{9}{2500} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{9}{1250}x+\frac{81}{6250000}=\frac{81}{6250000}$$

Tauwehea x^{2}-\frac{9}{1250}x+\frac{81}{6250000}. 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}.

$$\left(x-\frac{9}{2500}\right)^{2}=\frac{81}{6250000}$$

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

$$\sqrt{\left(x-\frac{9}{2500}\right)^{2}}=\sqrt{\frac{81}{6250000}}$$

Whakarūnātia.

$$x-\frac{9}{2500}=\frac{9}{2500} x-\frac{9}{2500}=-\frac{9}{2500}$$

Me tāpiri \frac{9}{2500} ki ngā taha e rua o te whārite.

$$x=\frac{9}{1250} x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{9}{1250}$$