Whakaoti i te 14x-21x^2

$$14 x - 21 x ^ { 2 }$$

Tauwehe

$$7x\left(2-3x\right)$$

Ngā Upane Otinga

Tauwehea te 7.

$$7\left(2x-3x^{2}\right)$$

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$7x\left(-3x+2\right)$$

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.

$$-21x^{2}+14x=0$$

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.

$$x=\frac{-14±\sqrt{14^{2}}}{2\left(-21\right)}$$

Tuhia te pūtakerua o te 14^{2}.

$$x=\frac{-14±14}{2\left(-21\right)}$$

Whakareatia 2 ki te -21.

$$x=\frac{-14±14}{-42}$$

Nā, me whakaoti te whārite x=\frac{-14±14}{-42} ina he tāpiri te ±. Tāpiri -14 ki te 14.

$$x=\frac{0}{-42}$$

Whakawehe 0 ki te -42.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-14±14}{-42} ina he tango te ±. Tango 14 mai i -14.

$$x=-\frac{28}{-42}$$

Whakahekea te hautanga \frac{-28}{-42} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

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

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

$$-21x^{2}+14x=-21x\left(x-\frac{2}{3}\right)$$

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.

$$-21x^{2}+14x=-21x\times \frac{-3x+2}{-3}$$

Whakakorea atu te tauwehe pūnoa nui rawa 3 i roto i te -21 me te -3.

$$-21x^{2}+14x=7x\left(-3x+2\right)$$

Aromātai

$$7x\left(2-3x\right)$$