Whakaoti i te 18n^2-909n

$$18 n ^ { 2 } - 909 n$$

Tauwehe

$$9n\left(2n-101\right)$$

Ngā Upane Otinga

Tauwehea te 9.

$$9\left(2n^{2}-101n\right)$$

Whakaarohia te 2n^{2}-101n. Tauwehea te n.

$$n\left(2n-101\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$9n\left(2n-101\right)$$

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.

$$18n^{2}-909n=0$$

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.

$$n=\frac{-\left(-909\right)±\sqrt{\left(-909\right)^{2}}}{2\times 18}$$

Tuhia te pūtakerua o te \left(-909\right)^{2}.

$$n=\frac{-\left(-909\right)±909}{2\times 18}$$

Ko te tauaro o -909 ko 909.

$$n=\frac{909±909}{2\times 18}$$

Whakareatia 2 ki te 18.

$$n=\frac{909±909}{36}$$

Nā, me whakaoti te whārite n=\frac{909±909}{36} ina he tāpiri te ±. Tāpiri 909 ki te 909.

$$n=\frac{1818}{36}$$

Whakahekea te hautanga \frac{1818}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 18.

$$n=\frac{101}{2}$$

Nā, me whakaoti te whārite n=\frac{909±909}{36} ina he tango te ±. Tango 909 mai i 909.

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

Whakawehe 0 ki te 36.

$$n=0$$

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{101}{2} mō te x_{1} me te 0 mō te x_{2}.

$$18n^{2}-909n=18\left(n-\frac{101}{2}\right)n$$

Tango \frac{101}{2} mai i n 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.

$$18n^{2}-909n=18\times \frac{2n-101}{2}n$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 18 me te 2.

$$18n^{2}-909n=9\left(2n-101\right)n$$

Aromātai

$$9n\left(2n-101\right)$$