Whakaoti i te 50q^2-60q+18

$$50 q ^ { 2 } - 60 q + 18$$

Tauwehe

$$2\left(5q-3\right)^{2}$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(25q^{2}-30q+9\right)$$

Whakaarohia te 25q^{2}-30q+9. Whakamahia te tikanga tātai pūrua pā, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, ina a=5q, ina b=3.

$$\left(5q-3\right)^{2}$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(5q-3\right)^{2}$$

Ngā Upane Whakamahi Tauwehe o te Pūrua Huarua

Ko te tikanga tātai o tēnei huatoru he pūrua huatoru, ka whakareatia pea e tētahi tauwehe pātahi. Ka taea ngā pūrua huatoru te tauwehe mā te kimi i ngā pūtakerua o ngā kīanga tau ārahi, autō hoki.

$$factor(50q^{2}-60q+18)$$

Kimihia te tauwehe pātahi nui rawa o ngā tau whakarea.

$$gcf(50,-60,18)=2$$

Tauwehea te 2.

$$2\left(25q^{2}-30q+9\right)$$

Kimihia te pūtakerua o te kīanga tau ārahi, 25q^{2}.

$$\sqrt{25q^{2}}=5q$$

Kimihia te pūtakerua o te kīanga tau autō, 9.

$$\sqrt{9}=3$$

Ko te pūrua huatoru te pūrua o te huarua ko te tapeke tērā, te huatango rānei o ngā pūtakerua o ngā kīanga tau ārahi, autō hoki, e whakaritea ai te tohu e te tohu o te kīanga tau waenga o te pūrua huatoru.

$$2\left(5q-3\right)^{2}$$

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.

$$50q^{2}-60q+18=0$$

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.

$$q=\frac{-\left(-60\right)±\sqrt{\left(-60\right)^{2}-4\times 50\times 18}}{2\times 50}$$

Pūrua -60.

$$q=\frac{-\left(-60\right)±\sqrt{3600-4\times 50\times 18}}{2\times 50}$$

Whakareatia -4 ki te 50.

$$q=\frac{-\left(-60\right)±\sqrt{3600-200\times 18}}{2\times 50}$$

Whakareatia -200 ki te 18.

$$q=\frac{-\left(-60\right)±\sqrt{3600-3600}}{2\times 50}$$

Tāpiri 3600 ki te -3600.

$$q=\frac{-\left(-60\right)±\sqrt{0}}{2\times 50}$$

Tuhia te pūtakerua o te 0.

$$q=\frac{-\left(-60\right)±0}{2\times 50}$$

Ko te tauaro o -60 ko 60.

$$q=\frac{60±0}{2\times 50}$$

Whakareatia 2 ki te 50.

$$q=\frac{60±0}{100}$$

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{3}{5} mō te x_{1} me te \frac{3}{5} mō te x_{2}.

$$50q^{2}-60q+18=50\left(q-\frac{3}{5}\right)\left(q-\frac{3}{5}\right)$$

Tango \frac{3}{5} mai i q 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.

$$50q^{2}-60q+18=50\times \frac{5q-3}{5}\left(q-\frac{3}{5}\right)$$

Tango \frac{3}{5} mai i q 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.

$$50q^{2}-60q+18=50\times \frac{5q-3}{5}\times \frac{5q-3}{5}$$

Whakareatia \frac{5q-3}{5} ki te \frac{5q-3}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$50q^{2}-60q+18=50\times \frac{\left(5q-3\right)\left(5q-3\right)}{5\times 5}$$

Whakareatia 5 ki te 5.

$$50q^{2}-60q+18=50\times \frac{\left(5q-3\right)\left(5q-3\right)}{25}$$

Whakakorea atu te tauwehe pūnoa nui rawa 25 i roto i te 50 me te 25.

$$50q^{2}-60q+18=2\left(5q-3\right)\left(5q-3\right)$$

Aromātai

$$2\left(5q-3\right)^{2}$$