Whakaoti i te 100x^2-90x+18=0

$$100 x ^ { 2 } - 90 x + 18 = 0$$

Whakaoti mō x

$$x=\frac{3}{10}=0.3$$

$$x=\frac{3}{5}=0.6$$

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.

$$100x^{2}-90x+18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 100 mō a, -90 mō b, me 18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-90\right)±\sqrt{\left(-90\right)^{2}-4\times 100\times 18}}{2\times 100}$$

Pūrua -90.

$$x=\frac{-\left(-90\right)±\sqrt{8100-4\times 100\times 18}}{2\times 100}$$

Whakareatia -4 ki te 100.

$$x=\frac{-\left(-90\right)±\sqrt{8100-400\times 18}}{2\times 100}$$

Whakareatia -400 ki te 18.

$$x=\frac{-\left(-90\right)±\sqrt{8100-7200}}{2\times 100}$$

Tāpiri 8100 ki te -7200.

$$x=\frac{-\left(-90\right)±\sqrt{900}}{2\times 100}$$

Tuhia te pūtakerua o te 900.

$$x=\frac{-\left(-90\right)±30}{2\times 100}$$

Ko te tauaro o -90 ko 90.

$$x=\frac{90±30}{2\times 100}$$

Whakareatia 2 ki te 100.

$$x=\frac{90±30}{200}$$

Nā, me whakaoti te whārite x=\frac{90±30}{200} ina he tāpiri te ±. Tāpiri 90 ki te 30.

$$x=\frac{120}{200}$$

Whakahekea te hautanga \frac{120}{200} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 40.

$$x=\frac{3}{5}$$

Nā, me whakaoti te whārite x=\frac{90±30}{200} ina he tango te ±. Tango 30 mai i 90.

$$x=\frac{60}{200}$$

Whakahekea te hautanga \frac{60}{200} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 20.

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

Kua oti te whārite te whakatau.

$$x=\frac{3}{5} x=\frac{3}{10}$$

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.

$$100x^{2}-90x+18=0$$

Me tango 18 mai i ngā taha e rua o te whārite.

$$100x^{2}-90x+18-18=-18$$

Mā te tango i te 18 i a ia ake anō ka toe ko te 0.

$$100x^{2}-90x=-18$$

Whakawehea ngā taha e rua ki te 100.

$$\frac{100x^{2}-90x}{100}=-\frac{18}{100}$$

Mā te whakawehe ki te 100 ka wetekia te whakareanga ki te 100.

$$x^{2}+\left(-\frac{90}{100}\right)x=-\frac{18}{100}$$

Whakahekea te hautanga \frac{-90}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$x^{2}-\frac{9}{10}x=-\frac{18}{100}$$

Whakahekea te hautanga \frac{-18}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{9}{10}x=-\frac{9}{50}$$

Whakawehea te -\frac{9}{10}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{20}. Nā, tāpiria te pūrua o te -\frac{9}{20} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{9}{10}x+\left(-\frac{9}{20}\right)^{2}=-\frac{9}{50}+\left(-\frac{9}{20}\right)^{2}$$

Pūruatia -\frac{9}{20} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{9}{10}x+\frac{81}{400}=-\frac{9}{50}+\frac{81}{400}$$

Tāpiri -\frac{9}{50} ki te \frac{81}{400} 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.

$$x^{2}-\frac{9}{10}x+\frac{81}{400}=\frac{9}{400}$$

Tauwehea x^{2}-\frac{9}{10}x+\frac{81}{400}. 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}.

$$\left(x-\frac{9}{20}\right)^{2}=\frac{9}{400}$$

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

$$\sqrt{\left(x-\frac{9}{20}\right)^{2}}=\sqrt{\frac{9}{400}}$$

Whakarūnātia.

$$x-\frac{9}{20}=\frac{3}{20} x-\frac{9}{20}=-\frac{3}{20}$$

Me tāpiri \frac{9}{20} ki ngā taha e rua o te whārite.

$$x=\frac{3}{5} x=\frac{3}{10}$$