Whakaoti i te 365x^2-7317x+365000=0

$$365 x ^ { 2 } - 7317 x + 365000 = 0$$

Whakaoti mō x (complex solution)

$$x=\frac{7317+\sqrt{479361511}i}{730}\approx 10.023287671+29.992227397i$$

$$x=\frac{-\sqrt{479361511}i+7317}{730}\approx 10.023287671-29.992227397i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$365x^{2}-7317x+365000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 365 mō a, -7317 mō b, me 365000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7317\right)±\sqrt{\left(-7317\right)^{2}-4\times 365\times 365000}}{2\times 365}$$

Pūrua -7317.

$$x=\frac{-\left(-7317\right)±\sqrt{53538489-4\times 365\times 365000}}{2\times 365}$$

Whakareatia -4 ki te 365.

$$x=\frac{-\left(-7317\right)±\sqrt{53538489-1460\times 365000}}{2\times 365}$$

Whakareatia -1460 ki te 365000.

$$x=\frac{-\left(-7317\right)±\sqrt{53538489-532900000}}{2\times 365}$$

Tāpiri 53538489 ki te -532900000.

$$x=\frac{-\left(-7317\right)±\sqrt{-479361511}}{2\times 365}$$

Tuhia te pūtakerua o te -479361511.

$$x=\frac{-\left(-7317\right)±\sqrt{479361511}i}{2\times 365}$$

Ko te tauaro o -7317 ko 7317.

$$x=\frac{7317±\sqrt{479361511}i}{2\times 365}$$

Whakareatia 2 ki te 365.

$$x=\frac{7317±\sqrt{479361511}i}{730}$$

Nā, me whakaoti te whārite x=\frac{7317±\sqrt{479361511}i}{730} ina he tāpiri te ±. Tāpiri 7317 ki te i\sqrt{479361511}.

$$x=\frac{7317+\sqrt{479361511}i}{730}$$

Nā, me whakaoti te whārite x=\frac{7317±\sqrt{479361511}i}{730} ina he tango te ±. Tango i\sqrt{479361511} mai i 7317.

$$x=\frac{-\sqrt{479361511}i+7317}{730}$$

Kua oti te whārite te whakatau.

$$x=\frac{7317+\sqrt{479361511}i}{730} x=\frac{-\sqrt{479361511}i+7317}{730}$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$365x^{2}-7317x+365000=0$$

Me tango 365000 mai i ngā taha e rua o te whārite.

$$365x^{2}-7317x+365000-365000=-365000$$

Mā te tango i te 365000 i a ia ake anō ka toe ko te 0.

$$365x^{2}-7317x=-365000$$

Whakawehea ngā taha e rua ki te 365.

$$\frac{365x^{2}-7317x}{365}=-\frac{365000}{365}$$

Mā te whakawehe ki te 365 ka wetekia te whakareanga ki te 365.

$$x^{2}-\frac{7317}{365}x=-\frac{365000}{365}$$

Whakawehe -365000 ki te 365.

$$x^{2}-\frac{7317}{365}x=-1000$$

Whakawehea te -\frac{7317}{365}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7317}{730}. Nā, tāpiria te pūrua o te -\frac{7317}{730} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{7317}{365}x+\left(-\frac{7317}{730}\right)^{2}=-1000+\left(-\frac{7317}{730}\right)^{2}$$

Pūruatia -\frac{7317}{730} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{7317}{365}x+\frac{53538489}{532900}=-1000+\frac{53538489}{532900}$$

Tāpiri -1000 ki te \frac{53538489}{532900}.

$$x^{2}-\frac{7317}{365}x+\frac{53538489}{532900}=-\frac{479361511}{532900}$$

Tauwehea x^{2}-\frac{7317}{365}x+\frac{53538489}{532900}. 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}.

$$\left(x-\frac{7317}{730}\right)^{2}=-\frac{479361511}{532900}$$

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

$$\sqrt{\left(x-\frac{7317}{730}\right)^{2}}=\sqrt{-\frac{479361511}{532900}}$$

Whakarūnātia.

$$x-\frac{7317}{730}=\frac{\sqrt{479361511}i}{730} x-\frac{7317}{730}=-\frac{\sqrt{479361511}i}{730}$$

Me tāpiri \frac{7317}{730} ki ngā taha e rua o te whārite.

$$x=\frac{7317+\sqrt{479361511}i}{730} x=\frac{-\sqrt{479361511}i+7317}{730}$$