Whakaoti i te 24x^2-28x

$$24 x ^ { 2 } - 28 x$$

Tauwehe

$$4x\left(6x-7\right)$$

Ngā Upane Otinga

Tauwehea te 4.

$$4\left(6x^{2}-7x\right)$$

Whakaarohia te 6x^{2}-7x. Tauwehea te x.

$$x\left(6x-7\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$4x\left(6x-7\right)$$

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.

$$24x^{2}-28x=0$$

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.

$$x=\frac{-\left(-28\right)±\sqrt{\left(-28\right)^{2}}}{2\times 24}$$

Tuhia te pūtakerua o te \left(-28\right)^{2}.

$$x=\frac{-\left(-28\right)±28}{2\times 24}$$

Ko te tauaro o -28 ko 28.

$$x=\frac{28±28}{2\times 24}$$

Whakareatia 2 ki te 24.

$$x=\frac{28±28}{48}$$

Nā, me whakaoti te whārite x=\frac{28±28}{48} ina he tāpiri te ±. Tāpiri 28 ki te 28.

$$x=\frac{56}{48}$$

Whakahekea te hautanga \frac{56}{48} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$x=\frac{7}{6}$$

Nā, me whakaoti te whārite x=\frac{28±28}{48} ina he tango te ±. Tango 28 mai i 28.

$$x=\frac{0}{48}$$

Whakawehe 0 ki te 48.

$$x=0$$

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{7}{6} mō te x_{1} me te 0 mō te x_{2}.

$$24x^{2}-28x=24\left(x-\frac{7}{6}\right)x$$

Tango \frac{7}{6} 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.

$$24x^{2}-28x=24\times \frac{6x-7}{6}x$$

Whakakorea atu te tauwehe pūnoa nui rawa 6 i roto i te 24 me te 6.

$$24x^{2}-28x=4\left(6x-7\right)x$$

Aromātai

$$4x\left(6x-7\right)$$