Whakaoti i te w^2-9w+14=

$$w ^ { 2 } - 9 w + 14 =$$

Tauwehe

$$\left(w-7\right)\left(w-2\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei w^{2}+aw+bw+14. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-9 ab=1\times 14=14$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 14.

$$-1,-14 -2,-7$$

Tātaihia te tapeke mō ia takirua.

$$-1-14=-15 -2-7=-9$$

Ko te otinga te takirua ka hoatu i te tapeke -9.

$$a=-7 b=-2$$

Tuhia anō te w^{2}-9w+14 hei \left(w^{2}-7w\right)+\left(-2w+14\right).

$$\left(w^{2}-7w\right)+\left(-2w+14\right)$$

Tauwehea te w i te tuatahi me te -2 i te rōpū tuarua.

$$w\left(w-7\right)-2\left(w-7\right)$$

Whakatauwehea atu te kīanga pātahi w-7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(w-7\right)\left(w-2\right)$$

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.

$$w^{2}-9w+14=0$$

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.

$$w=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 14}}{2}$$

Pūrua -9.

$$w=\frac{-\left(-9\right)±\sqrt{81-4\times 14}}{2}$$

Whakareatia -4 ki te 14.

$$w=\frac{-\left(-9\right)±\sqrt{81-56}}{2}$$

Tāpiri 81 ki te -56.

$$w=\frac{-\left(-9\right)±\sqrt{25}}{2}$$

Tuhia te pūtakerua o te 25.

$$w=\frac{-\left(-9\right)±5}{2}$$

Ko te tauaro o -9 ko 9.

$$w=\frac{9±5}{2}$$

Nā, me whakaoti te whārite w=\frac{9±5}{2} ina he tāpiri te ±. Tāpiri 9 ki te 5.

$$w=\frac{14}{2}$$

Whakawehe 14 ki te 2.

$$w=7$$

Nā, me whakaoti te whārite w=\frac{9±5}{2} ina he tango te ±. Tango 5 mai i 9.

$$w=\frac{4}{2}$$

Whakawehe 4 ki te 2.

$$w=2$$

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 7 mō te x_{1} me te 2 mō te x_{2}.

$$w^{2}-9w+14=\left(w-7\right)\left(w-2\right)$$

Aromātai

$$\left(w-7\right)\left(w-2\right)$$