Whakaoti i te 2w^2-18=0

$$2 { w }^{ 2 } -18=0$$

Whakaoti mō w

$$w=3$$

$$w=-3$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te 2.

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

Whakaarohia te w^{2}-9. Tuhia anō te w^{2}-9 hei w^{2}-3^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

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

$$w=3 w=-3$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 18 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

Whakawehea ngā taha e rua ki te 2.

$$w^{2}=\frac{18}{2}$$

Whakawehea te 18 ki te 2, kia riro ko 9.

$$w^{2}=9$$

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

$$w=3 w=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$2w^{2}-18=0$$

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

$$w=\frac{0±\sqrt{0^{2}-4\times 2\left(-18\right)}}{2\times 2}$$

Pūrua 0.

$$w=\frac{0±\sqrt{-4\times 2\left(-18\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$w=\frac{0±\sqrt{-8\left(-18\right)}}{2\times 2}$$

Whakareatia -8 ki te -18.

$$w=\frac{0±\sqrt{144}}{2\times 2}$$

Tuhia te pūtakerua o te 144.

$$w=\frac{0±12}{2\times 2}$$

Whakareatia 2 ki te 2.

$$w=\frac{0±12}{4}$$

Nā, me whakaoti te whārite w=\frac{0±12}{4} ina he tāpiri te ±. Whakawehe 12 ki te 4.

$$w=3$$

Nā, me whakaoti te whārite w=\frac{0±12}{4} ina he tango te ±. Whakawehe -12 ki te 4.

$$w=-3$$

Kua oti te whārite te whakatau.

$$w=3 w=-3$$