Whakaoti i te 100x^2-20x

$$100 x ^ { 2 } - 20 x$$

Tauwehe

$$20x\left(5x-1\right)$$

Ngā Upane Otinga

Tauwehea te 20.

$$20\left(5x^{2}-x\right)$$

Whakaarohia te 5x^{2}-x. Tauwehea te x.

$$x\left(5x-1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$20x\left(5x-1\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$100x^{2}-20x=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}}}{2\times 100}$$

Tuhia te pūtakerua o te \left(-20\right)^{2}.

$$x=\frac{-\left(-20\right)±20}{2\times 100}$$

Ko te tauaro o -20 ko 20.

$$x=\frac{20±20}{2\times 100}$$

Whakareatia 2 ki te 100.

$$x=\frac{20±20}{200}$$

Nā, me whakaoti te whārite x=\frac{20±20}{200} ina he tāpiri te ±. Tāpiri 20 ki te 20.

$$x=\frac{40}{200}$$

Whakahekea te hautanga \frac{40}{200} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 40.

$$x=\frac{1}{5}$$

Nā, me whakaoti te whārite x=\frac{20±20}{200} ina he tango te ±. Tango 20 mai i 20.

$$x=\frac{0}{200}$$

Whakawehe 0 ki te 200.

$$x=0$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te \frac{1}{5} mō te x_{1} me te 0 mō te x_{2}.

$$100x^{2}-20x=100\left(x-\frac{1}{5}\right)x$$

Tango \frac{1}{5} mai i x mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$100x^{2}-20x=100\times \frac{5x-1}{5}x$$

Whakakorea atu te tauwehe pūnoa nui rawa 5 i roto i te 100 me te 5.

$$100x^{2}-20x=20\left(5x-1\right)x$$

Aromātai

$$20x\left(5x-1\right)$$