Whakaoti i te 3w^2=-18w

$$3 w ^ { 2 } = - 18 w$$

Whakaoti mō w

$$w=-6$$

$$w=0$$

Ngā Upane Whakamahi Tauwehe

Me tāpiri te 18w ki ngā taha e rua.

$$3w^{2}+18w=0$$

Tauwehea te w.

$$w\left(3w+18\right)=0$$

Hei kimi otinga whārite, me whakaoti te w=0 me te 3w+18=0.

$$w=0 w=-6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 18w ki ngā taha e rua.

$$3w^{2}+18w=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 18 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-18±\sqrt{18^{2}}}{2\times 3}$$

Tuhia te pūtakerua o te 18^{2}.

$$w=\frac{-18±18}{2\times 3}$$

Whakareatia 2 ki te 3.

$$w=\frac{-18±18}{6}$$

Nā, me whakaoti te whārite w=\frac{-18±18}{6} ina he tāpiri te ±. Tāpiri -18 ki te 18.

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

Whakawehe 0 ki te 6.

$$w=0$$

Nā, me whakaoti te whārite w=\frac{-18±18}{6} ina he tango te ±. Tango 18 mai i -18.

$$w=-\frac{36}{6}$$

Whakawehe -36 ki te 6.

$$w=-6$$

Kua oti te whārite te whakatau.

$$w=0 w=-6$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 18w ki ngā taha e rua.

$$3w^{2}+18w=0$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3w^{2}+18w}{3}=\frac{0}{3}$$

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

$$w^{2}+\frac{18}{3}w=\frac{0}{3}$$

Whakawehe 18 ki te 3.

$$w^{2}+6w=\frac{0}{3}$$

Whakawehe 0 ki te 3.

$$w^{2}+6w=0$$

Whakawehea te 6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 3. Nā, tāpiria te pūrua o te 3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$w^{2}+6w+3^{2}=3^{2}$$

Pūrua 3.

$$w^{2}+6w+9=9$$

Tauwehea w^{2}+6w+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}.

$$\left(w+3\right)^{2}=9$$

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

$$\sqrt{\left(w+3\right)^{2}}=\sqrt{9}$$

Whakarūnātia.

$$w+3=3 w+3=-3$$

Me tango 3 mai i ngā taha e rua o te whārite.

$$w=0 w=-6$$