Whakaoti i te 100x^2=81

$$100 x ^ { 2 } = 81$$

Whakaoti mō x

$$x=\frac{9}{10}=0.9$$

$$x=-\frac{9}{10}=-0.9$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te 100.

$$x^{2}=\frac{81}{100}$$

Tangohia te \frac{81}{100} mai i ngā taha e rua.

$$x^{2}-\frac{81}{100}=0$$

Me whakarea ngā taha e rua ki te 100.

$$100x^{2}-81=0$$

Whakaarohia te 100x^{2}-81. Tuhia anō te 100x^{2}-81 hei \left(10x\right)^{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).

$$\left(10x-9\right)\left(10x+9\right)=0$$

Hei kimi otinga whārite, me whakaoti te 10x-9=0 me te 10x+9=0.

$$x=\frac{9}{10} x=-\frac{9}{10}$$

Ngā Upane mā te Kimi Pūtakerua

Whakawehea ngā taha e rua ki te 100.

$$x^{2}=\frac{81}{100}$$

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

$$x=\frac{9}{10} x=-\frac{9}{10}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ngā taha e rua ki te 100.

$$x^{2}=\frac{81}{100}$$

Tangohia te \frac{81}{100} mai i ngā taha e rua.

$$x^{2}-\frac{81}{100}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -\frac{81}{100} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{81}{100}\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{81}{100}\right)}}{2}$$

Whakareatia -4 ki te -\frac{81}{100}.

$$x=\frac{0±\sqrt{\frac{81}{25}}}{2}$$

Tuhia te pūtakerua o te \frac{81}{25}.

$$x=\frac{0±\frac{9}{5}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{9}{5}}{2} ina he tāpiri te ±.

$$x=\frac{9}{10}$$

Nā, me whakaoti te whārite x=\frac{0±\frac{9}{5}}{2} ina he tango te ±.

$$x=-\frac{9}{10}$$

Kua oti te whārite te whakatau.

$$x=\frac{9}{10} x=-\frac{9}{10}$$