Whakaoti i te 3w^2-27w=0

$$3 w ^ { 2 } - 27 w = 0$$

Whakaoti mō w

$$w=9$$

$$w=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te w.

$$w\left(3w-27\right)=0$$

Hei kimi otinga whārite, me whakaoti te w=0 me te 3w-27=0.

$$w=0 w=9$$

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.

$$3w^{2}-27w=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -27 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-\left(-27\right)±\sqrt{\left(-27\right)^{2}}}{2\times 3}$$

Tuhia te pūtakerua o te \left(-27\right)^{2}.

$$w=\frac{-\left(-27\right)±27}{2\times 3}$$

Ko te tauaro o -27 ko 27.

$$w=\frac{27±27}{2\times 3}$$

Whakareatia 2 ki te 3.

$$w=\frac{27±27}{6}$$

Nā, me whakaoti te whārite w=\frac{27±27}{6} ina he tāpiri te ±. Tāpiri 27 ki te 27.

$$w=\frac{54}{6}$$

Whakawehe 54 ki te 6.

$$w=9$$

Nā, me whakaoti te whārite w=\frac{27±27}{6} ina he tango te ±. Tango 27 mai i 27.

$$w=\frac{0}{6}$$

Whakawehe 0 ki te 6.

$$w=0$$

Kua oti te whārite te whakatau.

$$w=9 w=0$$

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.

$$3w^{2}-27w=0$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3w^{2}-27w}{3}=\frac{0}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$w^{2}+\left(-\frac{27}{3}\right)w=\frac{0}{3}$$

Whakawehe -27 ki te 3.

$$w^{2}-9w=\frac{0}{3}$$

Whakawehe 0 ki te 3.

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

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

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

Pūruatia -\frac{9}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$w^{2}-9w+\frac{81}{4}=\frac{81}{4}$$

Tauwehea w^{2}-9w+\frac{81}{4}. 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}.

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

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

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

Whakarūnātia.

$$w-\frac{9}{2}=\frac{9}{2} w-\frac{9}{2}=-\frac{9}{2}$$

Me tāpiri \frac{9}{2} ki ngā taha e rua o te whārite.

$$w=9 w=0$$