Whakaoti i te 18x^2-12x

$$18 { x }^{ 2 } -12x$$

Tauwehe

$$6x\left(3x-2\right)$$

Ngā Upane Otinga

Tauwehea te 6.

$$6\left(3x^{2}-2x\right)$$

Whakaarohia te 3x^{2}-2x. Tauwehea te x.

$$x\left(3x-2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$6x\left(3x-2\right)$$

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.

$$18x^{2}-12x=0$$

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.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2\times 18}$$

Tuhia te pūtakerua o te \left(-12\right)^{2}.

$$x=\frac{-\left(-12\right)±12}{2\times 18}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±12}{2\times 18}$$

Whakareatia 2 ki te 18.

$$x=\frac{12±12}{36}$$

Nā, me whakaoti te whārite x=\frac{12±12}{36} ina he tāpiri te ±. Tāpiri 12 ki te 12.

$$x=\frac{24}{36}$$

Whakahekea te hautanga \frac{24}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

$$x=\frac{2}{3}$$

Nā, me whakaoti te whārite x=\frac{12±12}{36} ina he tango te ±. Tango 12 mai i 12.

$$x=\frac{0}{36}$$

Whakawehe 0 ki te 36.

$$x=0$$

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{2}{3} mō te x_{1} me te 0 mō te x_{2}.

$$18x^{2}-12x=18\left(x-\frac{2}{3}\right)x$$

Tango \frac{2}{3} 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.

$$18x^{2}-12x=18\times \frac{3x-2}{3}x$$

Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te 18 me te 3.

$$18x^{2}-12x=6\left(3x-2\right)x$$

Aromātai

$$6x\left(3x-2\right)$$