Whakaoti i te 4x^2-324=0

$$4 x ^ { 2 } - 324 = 0$$

Whakaoti mō x

$$x=9$$

$$x=-9$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te 4.

$$x^{2}-81=0$$

Whakaarohia te x^{2}-81. Tuhia anō te x^{2}-81 hei x^{2}-9^{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).

$$\left(x-9\right)\left(x+9\right)=0$$

Hei kimi otinga whārite, me whakaoti te x-9=0 me te x+9=0.

$$x=9 x=-9$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 324 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$4x^{2}=324$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{324}{4}$$

Whakawehea te 324 ki te 4, kia riro ko 81.

$$x^{2}=81$$

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

$$x=9 x=-9$$

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.

$$4x^{2}-324=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 0 mō b, me -324 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-324\right)}}{2\times 4}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-324\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16\left(-324\right)}}{2\times 4}$$

Whakareatia -16 ki te -324.

$$x=\frac{0±\sqrt{5184}}{2\times 4}$$

Tuhia te pūtakerua o te 5184.

$$x=\frac{0±72}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±72}{8}$$

Nā, me whakaoti te whārite x=\frac{0±72}{8} ina he tāpiri te ±. Whakawehe 72 ki te 8.

$$x=9$$

Nā, me whakaoti te whārite x=\frac{0±72}{8} ina he tango te ±. Whakawehe -72 ki te 8.

$$x=-9$$

Kua oti te whārite te whakatau.

$$x=9 x=-9$$