Whakaoti i te 5975x^2+450125x-706653125=0

$$5975 x ^ { 2 } + 450125 x - 706653125 = 0$$

Whakaoti mō x

$$x = \frac{5 \sqrt{1093863821} - 18005}{478} \approx 308.290922127$$

$$x=\frac{-5\sqrt{1093863821}-18005}{478}\approx -383.62565016$$

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.

$$5975x^{2}+450125x-706653125=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5975 mō a, 450125 mō b, me -706653125 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-450125±\sqrt{450125^{2}-4\times 5975\left(-706653125\right)}}{2\times 5975}$$

Pūrua 450125.

$$x=\frac{-450125±\sqrt{202612515625-4\times 5975\left(-706653125\right)}}{2\times 5975}$$

Whakareatia -4 ki te 5975.

$$x=\frac{-450125±\sqrt{202612515625-23900\left(-706653125\right)}}{2\times 5975}$$

Whakareatia -23900 ki te -706653125.

$$x=\frac{-450125±\sqrt{202612515625+16889009687500}}{2\times 5975}$$

Tāpiri 202612515625 ki te 16889009687500.

$$x=\frac{-450125±\sqrt{17091622203125}}{2\times 5975}$$

Tuhia te pūtakerua o te 17091622203125.

$$x=\frac{-450125±125\sqrt{1093863821}}{2\times 5975}$$

Whakareatia 2 ki te 5975.

$$x=\frac{-450125±125\sqrt{1093863821}}{11950}$$

Nā, me whakaoti te whārite x=\frac{-450125±125\sqrt{1093863821}}{11950} ina he tāpiri te ±. Tāpiri -450125 ki te 125\sqrt{1093863821}.

$$x=\frac{125\sqrt{1093863821}-450125}{11950}$$

Whakawehe -450125+125\sqrt{1093863821} ki te 11950.

$$x=\frac{5\sqrt{1093863821}-18005}{478}$$

Nā, me whakaoti te whārite x=\frac{-450125±125\sqrt{1093863821}}{11950} ina he tango te ±. Tango 125\sqrt{1093863821} mai i -450125.

$$x=\frac{-125\sqrt{1093863821}-450125}{11950}$$

Whakawehe -450125-125\sqrt{1093863821} ki te 11950.

$$x=\frac{-5\sqrt{1093863821}-18005}{478}$$

Kua oti te whārite te whakatau.

$$x=\frac{5\sqrt{1093863821}-18005}{478} x=\frac{-5\sqrt{1093863821}-18005}{478}$$

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.

$$5975x^{2}+450125x-706653125=0$$

Me tāpiri 706653125 ki ngā taha e rua o te whārite.

$$5975x^{2}+450125x-706653125-\left(-706653125\right)=-\left(-706653125\right)$$

Mā te tango i te -706653125 i a ia ake anō ka toe ko te 0.

$$5975x^{2}+450125x=-\left(-706653125\right)$$

Tango -706653125 mai i 0.

$$5975x^{2}+450125x=706653125$$

Whakawehea ngā taha e rua ki te 5975.

$$\frac{5975x^{2}+450125x}{5975}=\frac{706653125}{5975}$$

Mā te whakawehe ki te 5975 ka wetekia te whakareanga ki te 5975.

$$x^{2}+\frac{450125}{5975}x=\frac{706653125}{5975}$$

Whakahekea te hautanga \frac{450125}{5975} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$x^{2}+\frac{18005}{239}x=\frac{706653125}{5975}$$

Whakahekea te hautanga \frac{706653125}{5975} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$x^{2}+\frac{18005}{239}x=\frac{28266125}{239}$$

Whakawehea te \frac{18005}{239}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{18005}{478}. Nā, tāpiria te pūrua o te \frac{18005}{478} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{18005}{239}x+\left(\frac{18005}{478}\right)^{2}=\frac{28266125}{239}+\left(\frac{18005}{478}\right)^{2}$$

Pūruatia \frac{18005}{478} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{18005}{239}x+\frac{324180025}{228484}=\frac{28266125}{239}+\frac{324180025}{228484}$$

Tāpiri \frac{28266125}{239} ki te \frac{324180025}{228484} 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.

$$x^{2}+\frac{18005}{239}x+\frac{324180025}{228484}=\frac{27346595525}{228484}$$

Tauwehea x^{2}+\frac{18005}{239}x+\frac{324180025}{228484}. 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}.

$$\left(x+\frac{18005}{478}\right)^{2}=\frac{27346595525}{228484}$$

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

$$\sqrt{\left(x+\frac{18005}{478}\right)^{2}}=\sqrt{\frac{27346595525}{228484}}$$

Whakarūnātia.

$$x+\frac{18005}{478}=\frac{5\sqrt{1093863821}}{478} x+\frac{18005}{478}=-\frac{5\sqrt{1093863821}}{478}$$

Me tango \frac{18005}{478} mai i ngā taha e rua o te whārite.

$$x=\frac{5\sqrt{1093863821}-18005}{478} x=\frac{-5\sqrt{1093863821}-18005}{478}$$