Whakaoti i te 4x^2-11x

$$4 x ^ { 2 } - 11 x$$

Tauwehe

$$x\left(4x-11\right)$$

Ngā Upane Otinga

Tauwehea te x.

$$x\left(4x-11\right)$$

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.

$$4x^{2}-11x=0$$

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.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}}}{2\times 4}$$

Tuhia te pūtakerua o te \left(-11\right)^{2}.

$$x=\frac{-\left(-11\right)±11}{2\times 4}$$

Ko te tauaro o -11 ko 11.

$$x=\frac{11±11}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{11±11}{8}$$

Nā, me whakaoti te whārite x=\frac{11±11}{8} ina he tāpiri te ±. Tāpiri 11 ki te 11.

$$x=\frac{22}{8}$$

Whakahekea te hautanga \frac{22}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{11}{4}$$

Nā, me whakaoti te whārite x=\frac{11±11}{8} ina he tango te ±. Tango 11 mai i 11.

$$x=\frac{0}{8}$$

Whakawehe 0 ki te 8.

$$x=0$$

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{11}{4} mō te x_{1} me te 0 mō te x_{2}.

$$4x^{2}-11x=4\left(x-\frac{11}{4}\right)x$$

Tango \frac{11}{4} 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.

$$4x^{2}-11x=4\times \frac{4x-11}{4}x$$

Whakakorea atu te tauwehe pūnoa nui rawa 4 i roto i te 4 me te 4.

$$4x^{2}-11x=\left(4x-11\right)x$$

Aromātai

$$x\left(4x-11\right)$$