Whakaoti i te 300x^2+800x-800=0

$$300 x ^ { 2 } + 800 x - 800 = 0$$

Whakaoti mō x

$$x=\frac{2\sqrt{10}-4}{3}\approx 0.774851773$$

$$x=\frac{-2\sqrt{10}-4}{3}\approx -3.44151844$$

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.

$$300x^{2}+800x-800=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 300 mō a, 800 mō b, me -800 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-800±\sqrt{800^{2}-4\times 300\left(-800\right)}}{2\times 300}$$

Pūrua 800.

$$x=\frac{-800±\sqrt{640000-4\times 300\left(-800\right)}}{2\times 300}$$

Whakareatia -4 ki te 300.

$$x=\frac{-800±\sqrt{640000-1200\left(-800\right)}}{2\times 300}$$

Whakareatia -1200 ki te -800.

$$x=\frac{-800±\sqrt{640000+960000}}{2\times 300}$$

Tāpiri 640000 ki te 960000.

$$x=\frac{-800±\sqrt{1600000}}{2\times 300}$$

Tuhia te pūtakerua o te 1600000.

$$x=\frac{-800±400\sqrt{10}}{2\times 300}$$

Whakareatia 2 ki te 300.

$$x=\frac{-800±400\sqrt{10}}{600}$$

Nā, me whakaoti te whārite x=\frac{-800±400\sqrt{10}}{600} ina he tāpiri te ±. Tāpiri -800 ki te 400\sqrt{10}.

$$x=\frac{400\sqrt{10}-800}{600}$$

Whakawehe -800+400\sqrt{10} ki te 600.

$$x=\frac{2\sqrt{10}-4}{3}$$

Nā, me whakaoti te whārite x=\frac{-800±400\sqrt{10}}{600} ina he tango te ±. Tango 400\sqrt{10} mai i -800.

$$x=\frac{-400\sqrt{10}-800}{600}$$

Whakawehe -800-400\sqrt{10} ki te 600.

$$x=\frac{-2\sqrt{10}-4}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{10}-4}{3} x=\frac{-2\sqrt{10}-4}{3}$$

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.

$$300x^{2}+800x-800=0$$

Me tāpiri 800 ki ngā taha e rua o te whārite.

$$300x^{2}+800x-800-\left(-800\right)=-\left(-800\right)$$

Mā te tango i te -800 i a ia ake anō ka toe ko te 0.

$$300x^{2}+800x=-\left(-800\right)$$

Tango -800 mai i 0.

$$300x^{2}+800x=800$$

Whakawehea ngā taha e rua ki te 300.

$$\frac{300x^{2}+800x}{300}=\frac{800}{300}$$

Mā te whakawehe ki te 300 ka wetekia te whakareanga ki te 300.

$$x^{2}+\frac{800}{300}x=\frac{800}{300}$$

Whakahekea te hautanga \frac{800}{300} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 100.

$$x^{2}+\frac{8}{3}x=\frac{800}{300}$$

Whakahekea te hautanga \frac{800}{300} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 100.

$$x^{2}+\frac{8}{3}x=\frac{8}{3}$$

Whakawehea te \frac{8}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{4}{3}. Nā, tāpiria te pūrua o te \frac{4}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{8}{3}x+\left(\frac{4}{3}\right)^{2}=\frac{8}{3}+\left(\frac{4}{3}\right)^{2}$$

Pūruatia \frac{4}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{8}{3}x+\frac{16}{9}=\frac{8}{3}+\frac{16}{9}$$

Tāpiri \frac{8}{3} ki te \frac{16}{9} 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.

$$x^{2}+\frac{8}{3}x+\frac{16}{9}=\frac{40}{9}$$

Tauwehea x^{2}+\frac{8}{3}x+\frac{16}{9}. 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}.

$$\left(x+\frac{4}{3}\right)^{2}=\frac{40}{9}$$

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

$$\sqrt{\left(x+\frac{4}{3}\right)^{2}}=\sqrt{\frac{40}{9}}$$

Whakarūnātia.

$$x+\frac{4}{3}=\frac{2\sqrt{10}}{3} x+\frac{4}{3}=-\frac{2\sqrt{10}}{3}$$

Me tango \frac{4}{3} mai i ngā taha e rua o te whārite.

$$x=\frac{2\sqrt{10}-4}{3} x=\frac{-2\sqrt{10}-4}{3}$$