Whakaoti i te 18q^2+6q

$$18 q ^ { 2 } + 6 q$$

Tauwehe

$$6q\left(3q+1\right)$$

Ngā Upane Otinga

Tauwehea te 6.

$$6\left(3q^{2}+q\right)$$

Whakaarohia te 3q^{2}+q. Tauwehea te q.

$$q\left(3q+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$6q\left(3q+1\right)$$

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.

$$18q^{2}+6q=0$$

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.

$$q=\frac{-6±\sqrt{6^{2}}}{2\times 18}$$

Tuhia te pūtakerua o te 6^{2}.

$$q=\frac{-6±6}{2\times 18}$$

Whakareatia 2 ki te 18.

$$q=\frac{-6±6}{36}$$

Nā, me whakaoti te whārite q=\frac{-6±6}{36} ina he tāpiri te ±. Tāpiri -6 ki te 6.

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

Whakawehe 0 ki te 36.

$$q=0$$

Nā, me whakaoti te whārite q=\frac{-6±6}{36} ina he tango te ±. Tango 6 mai i -6.

$$q=-\frac{12}{36}$$

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

$$q=-\frac{1}{3}$$

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{1}{3} mō te x_{2}.

$$18q^{2}+6q=18q\left(q-\left(-\frac{1}{3}\right)\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$18q^{2}+6q=18q\left(q+\frac{1}{3}\right)$$

Tāpiri \frac{1}{3} ki te q mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$18q^{2}+6q=18q\times \frac{3q+1}{3}$$

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

$$18q^{2}+6q=6q\left(3q+1\right)$$

Aromātai

$$6q\left(3q+1\right)$$