Whakaoti i te 4x^2-16=0

$$4 { x }^{ 2 } -16=0$$

Whakaoti mō x

$$x=2$$

$$x=-2$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te 4.

$$x^{2}-4=0$$

Whakaarohia te x^{2}-4. Tuhia anō te x^{2}-4 hei x^{2}-2^{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).

$$\left(x-2\right)\left(x+2\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-2=0 me te x+2=0.

$$x=2 x=-2$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 16 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$4x^{2}=16$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{16}{4}$$

Whakawehea te 16 ki te 4, kia riro ko 4.

$$x^{2}=4$$

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

$$x=2 x=-2$$

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.

$$4x^{2}-16=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 0 mō b, me -16 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-16\right)}}{2\times 4}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-16\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16\left(-16\right)}}{2\times 4}$$

Whakareatia -16 ki te -16.

$$x=\frac{0±\sqrt{256}}{2\times 4}$$

Tuhia te pūtakerua o te 256.

$$x=\frac{0±16}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±16}{8}$$

Nā, me whakaoti te whārite x=\frac{0±16}{8} ina he tāpiri te ±. Whakawehe 16 ki te 8.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{0±16}{8} ina he tango te ±. Whakawehe -16 ki te 8.

$$x=-2$$

Kua oti te whārite te whakatau.

$$x=2 x=-2$$