Whakaoti i te 2000000divx+204x=1600000

$$2000000 \div x+204x=1600000$$

Whakaoti mō x

$$x = \frac{500 \sqrt{159898} + 200000}{51} \approx 7841.88705562$$

$$x = \frac{200000 - 500 \sqrt{159898}}{51} \approx 1.250199282$$

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.

$$2000000+204xx=1600000x$$

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

$$2000000+204x^{2}=1600000x$$

Tangohia te 1600000x mai i ngā taha e rua.

$$2000000+204x^{2}-1600000x=0$$

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.

$$204x^{2}-1600000x+2000000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 204 mō a, -1600000 mō b, me 2000000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1600000\right)±\sqrt{\left(-1600000\right)^{2}-4\times 204\times 2000000}}{2\times 204}$$

Pūrua -1600000.

$$x=\frac{-\left(-1600000\right)±\sqrt{2560000000000-4\times 204\times 2000000}}{2\times 204}$$

Whakareatia -4 ki te 204.

$$x=\frac{-\left(-1600000\right)±\sqrt{2560000000000-816\times 2000000}}{2\times 204}$$

Whakareatia -816 ki te 2000000.

$$x=\frac{-\left(-1600000\right)±\sqrt{2560000000000-1632000000}}{2\times 204}$$

Tāpiri 2560000000000 ki te -1632000000.

$$x=\frac{-\left(-1600000\right)±\sqrt{2558368000000}}{2\times 204}$$

Tuhia te pūtakerua o te 2558368000000.

$$x=\frac{-\left(-1600000\right)±4000\sqrt{159898}}{2\times 204}$$

Ko te tauaro o -1600000 ko 1600000.

$$x=\frac{1600000±4000\sqrt{159898}}{2\times 204}$$

Whakareatia 2 ki te 204.

$$x=\frac{1600000±4000\sqrt{159898}}{408}$$

Nā, me whakaoti te whārite x=\frac{1600000±4000\sqrt{159898}}{408} ina he tāpiri te ±. Tāpiri 1600000 ki te 4000\sqrt{159898}.

$$x=\frac{4000\sqrt{159898}+1600000}{408}$$

Whakawehe 1600000+4000\sqrt{159898} ki te 408.

$$x=\frac{500\sqrt{159898}+200000}{51}$$

Nā, me whakaoti te whārite x=\frac{1600000±4000\sqrt{159898}}{408} ina he tango te ±. Tango 4000\sqrt{159898} mai i 1600000.

$$x=\frac{1600000-4000\sqrt{159898}}{408}$$

Whakawehe 1600000-4000\sqrt{159898} ki te 408.

$$x=\frac{200000-500\sqrt{159898}}{51}$$

Kua oti te whārite te whakatau.

$$x=\frac{500\sqrt{159898}+200000}{51} x=\frac{200000-500\sqrt{159898}}{51}$$

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.

$$2000000+204xx=1600000x$$

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

$$2000000+204x^{2}=1600000x$$

Tangohia te 1600000x mai i ngā taha e rua.

$$2000000+204x^{2}-1600000x=0$$

Tangohia te 2000000 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$204x^{2}-1600000x=-2000000$$

Whakawehea ngā taha e rua ki te 204.

$$\frac{204x^{2}-1600000x}{204}=-\frac{2000000}{204}$$

Mā te whakawehe ki te 204 ka wetekia te whakareanga ki te 204.

$$x^{2}+\left(-\frac{1600000}{204}\right)x=-\frac{2000000}{204}$$

Whakahekea te hautanga \frac{-1600000}{204} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{400000}{51}x=-\frac{2000000}{204}$$

Whakahekea te hautanga \frac{-2000000}{204} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{400000}{51}x=-\frac{500000}{51}$$

Whakawehea te -\frac{400000}{51}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{200000}{51}. Nā, tāpiria te pūrua o te -\frac{200000}{51} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{400000}{51}x+\left(-\frac{200000}{51}\right)^{2}=-\frac{500000}{51}+\left(-\frac{200000}{51}\right)^{2}$$

Pūruatia -\frac{200000}{51} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{400000}{51}x+\frac{40000000000}{2601}=-\frac{500000}{51}+\frac{40000000000}{2601}$$

Tāpiri -\frac{500000}{51} ki te \frac{40000000000}{2601} 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.

$$x^{2}-\frac{400000}{51}x+\frac{40000000000}{2601}=\frac{39974500000}{2601}$$

Tauwehea x^{2}-\frac{400000}{51}x+\frac{40000000000}{2601}. 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}.

$$\left(x-\frac{200000}{51}\right)^{2}=\frac{39974500000}{2601}$$

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

$$\sqrt{\left(x-\frac{200000}{51}\right)^{2}}=\sqrt{\frac{39974500000}{2601}}$$

Whakarūnātia.

$$x-\frac{200000}{51}=\frac{500\sqrt{159898}}{51} x-\frac{200000}{51}=-\frac{500\sqrt{159898}}{51}$$

Me tāpiri \frac{200000}{51} ki ngā taha e rua o te whārite.

$$x=\frac{500\sqrt{159898}+200000}{51} x=\frac{200000-500\sqrt{159898}}{51}$$