Whakaoti i te 2m^2-9m=0

$$2 m ^ { 2 } - 9 m = 0$$

Whakaoti mō m

$$m = \frac{9}{2} = 4\frac{1}{2} = 4.5$$

$$m=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te m.

$$m\left(2m-9\right)=0$$

Hei kimi otinga whārite, me whakaoti te m=0 me te 2m-9=0.

$$m=0 m=\frac{9}{2}$$

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.

$$2m^{2}-9m=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -9 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}}}{2\times 2}$$

Tuhia te pūtakerua o te \left(-9\right)^{2}.

$$m=\frac{-\left(-9\right)±9}{2\times 2}$$

Ko te tauaro o -9 ko 9.

$$m=\frac{9±9}{2\times 2}$$

Whakareatia 2 ki te 2.

$$m=\frac{9±9}{4}$$

Nā, me whakaoti te whārite m=\frac{9±9}{4} ina he tāpiri te ±. Tāpiri 9 ki te 9.

$$m=\frac{18}{4}$$

Whakahekea te hautanga \frac{18}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$m=\frac{9}{2}$$

Nā, me whakaoti te whārite m=\frac{9±9}{4} ina he tango te ±. Tango 9 mai i 9.

$$m=\frac{0}{4}$$

Whakawehe 0 ki te 4.

$$m=0$$

Kua oti te whārite te whakatau.

$$m=\frac{9}{2} m=0$$

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.

$$2m^{2}-9m=0$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2m^{2}-9m}{2}=\frac{0}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$m^{2}-\frac{9}{2}m=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$m^{2}-\frac{9}{2}m=0$$

Whakawehea te -\frac{9}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{4}. Nā, tāpiria te pūrua o te -\frac{9}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$m^{2}-\frac{9}{2}m+\left(-\frac{9}{4}\right)^{2}=\left(-\frac{9}{4}\right)^{2}$$

Pūruatia -\frac{9}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$m^{2}-\frac{9}{2}m+\frac{81}{16}=\frac{81}{16}$$

Tauwehea m^{2}-\frac{9}{2}m+\frac{81}{16}. 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}.

$$\left(m-\frac{9}{4}\right)^{2}=\frac{81}{16}$$

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

$$\sqrt{\left(m-\frac{9}{4}\right)^{2}}=\sqrt{\frac{81}{16}}$$

Whakarūnātia.

$$m-\frac{9}{4}=\frac{9}{4} m-\frac{9}{4}=-\frac{9}{4}$$

Me tāpiri \frac{9}{4} ki ngā taha e rua o te whārite.

$$m=\frac{9}{2} m=0$$