Whakaoti i te 12x^2-160x+400=0

$$12 { x }^{ 2 } -160x+400 = 0$$

Whakaoti mō x

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

$$x=10$$

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.

$$12x^{2}-160x+400=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 12 mō a, -160 mō b, me 400 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-160\right)±\sqrt{\left(-160\right)^{2}-4\times 12\times 400}}{2\times 12}$$

Pūrua -160.

$$x=\frac{-\left(-160\right)±\sqrt{25600-4\times 12\times 400}}{2\times 12}$$

Whakareatia -4 ki te 12.

$$x=\frac{-\left(-160\right)±\sqrt{25600-48\times 400}}{2\times 12}$$

Whakareatia -48 ki te 400.

$$x=\frac{-\left(-160\right)±\sqrt{25600-19200}}{2\times 12}$$

Tāpiri 25600 ki te -19200.

$$x=\frac{-\left(-160\right)±\sqrt{6400}}{2\times 12}$$

Tuhia te pūtakerua o te 6400.

$$x=\frac{-\left(-160\right)±80}{2\times 12}$$

Ko te tauaro o -160 ko 160.

$$x=\frac{160±80}{2\times 12}$$

Whakareatia 2 ki te 12.

$$x=\frac{160±80}{24}$$

Nā, me whakaoti te whārite x=\frac{160±80}{24} ina he tāpiri te ±. Tāpiri 160 ki te 80.

$$x=\frac{240}{24}$$

Whakawehe 240 ki te 24.

$$x=10$$

Nā, me whakaoti te whārite x=\frac{160±80}{24} ina he tango te ±. Tango 80 mai i 160.

$$x=\frac{80}{24}$$

Whakahekea te hautanga \frac{80}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$x=\frac{10}{3}$$

Kua oti te whārite te whakatau.

$$x=10 x=\frac{10}{3}$$

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.

$$12x^{2}-160x+400=0$$

Me tango 400 mai i ngā taha e rua o te whārite.

$$12x^{2}-160x+400-400=-400$$

Mā te tango i te 400 i a ia ake anō ka toe ko te 0.

$$12x^{2}-160x=-400$$

Whakawehea ngā taha e rua ki te 12.

$$\frac{12x^{2}-160x}{12}=-\frac{400}{12}$$

Mā te whakawehe ki te 12 ka wetekia te whakareanga ki te 12.

$$x^{2}+\left(-\frac{160}{12}\right)x=-\frac{400}{12}$$

Whakahekea te hautanga \frac{-160}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{40}{3}x=-\frac{400}{12}$$

Whakahekea te hautanga \frac{-400}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{40}{3}x=-\frac{100}{3}$$

Whakawehea te -\frac{40}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{20}{3}. Nā, tāpiria te pūrua o te -\frac{20}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{40}{3}x+\left(-\frac{20}{3}\right)^{2}=-\frac{100}{3}+\left(-\frac{20}{3}\right)^{2}$$

Pūruatia -\frac{20}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{40}{3}x+\frac{400}{9}=-\frac{100}{3}+\frac{400}{9}$$

Tāpiri -\frac{100}{3} ki te \frac{400}{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.

$$x^{2}-\frac{40}{3}x+\frac{400}{9}=\frac{100}{9}$$

Tauwehea x^{2}-\frac{40}{3}x+\frac{400}{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}.

$$\left(x-\frac{20}{3}\right)^{2}=\frac{100}{9}$$

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

$$\sqrt{\left(x-\frac{20}{3}\right)^{2}}=\sqrt{\frac{100}{9}}$$

Whakarūnātia.

$$x-\frac{20}{3}=\frac{10}{3} x-\frac{20}{3}=-\frac{10}{3}$$

Me tāpiri \frac{20}{3} ki ngā taha e rua o te whārite.

$$x=10 x=\frac{10}{3}$$