Whakaoti i te 10x^2-18x+0=0

$$10 { x }^{ 2 } -18x+0 = 0$$

Whakaoti mō x

$$x = \frac{9}{5} = 1\frac{4}{5} = 1.8$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Ko te tau i tāpiria he kore ka hua koia tonu.

$$10x^{2}-18x=0$$

Tauwehea te x.

$$x\left(10x-18\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 10x-18=0.

$$x=0 x=\frac{9}{5}$$

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.

$$10x^{2}-18x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 10 mō a, -18 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}}}{2\times 10}$$

Tuhia te pūtakerua o te \left(-18\right)^{2}.

$$x=\frac{-\left(-18\right)±18}{2\times 10}$$

Ko te tauaro o -18 ko 18.

$$x=\frac{18±18}{2\times 10}$$

Whakareatia 2 ki te 10.

$$x=\frac{18±18}{20}$$

Nā, me whakaoti te whārite x=\frac{18±18}{20} ina he tāpiri te ±. Tāpiri 18 ki te 18.

$$x=\frac{36}{20}$$

Whakahekea te hautanga \frac{36}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{9}{5}$$

Nā, me whakaoti te whārite x=\frac{18±18}{20} ina he tango te ±. Tango 18 mai i 18.

$$x=\frac{0}{20}$$

Whakawehe 0 ki te 20.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{9}{5} x=0$$

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.

$$10x^{2}-18x=0$$

Whakawehea ngā taha e rua ki te 10.

$$\frac{10x^{2}-18x}{10}=\frac{0}{10}$$

Mā te whakawehe ki te 10 ka wetekia te whakareanga ki te 10.

$$x^{2}+\left(-\frac{18}{10}\right)x=\frac{0}{10}$$

Whakahekea te hautanga \frac{-18}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{9}{5}x=\frac{0}{10}$$

Whakawehe 0 ki te 10.

$$x^{2}-\frac{9}{5}x=0$$

Whakawehea te -\frac{9}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{10}. Nā, tāpiria te pūrua o te -\frac{9}{10} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{9}{5}x+\left(-\frac{9}{10}\right)^{2}=\left(-\frac{9}{10}\right)^{2}$$

Pūruatia -\frac{9}{10} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{9}{5}x+\frac{81}{100}=\frac{81}{100}$$

Tauwehea te x^{2}-\frac{9}{5}x+\frac{81}{100}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{9}{10}\right)^{2}=\frac{81}{100}$$

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

$$\sqrt{\left(x-\frac{9}{10}\right)^{2}}=\sqrt{\frac{81}{100}}$$

Whakarūnātia.

$$x-\frac{9}{10}=\frac{9}{10} x-\frac{9}{10}=-\frac{9}{10}$$

Me tāpiri \frac{9}{10} ki ngā taha e rua o te whārite.

$$x=\frac{9}{5} x=0$$