Whakaoti i te 6w^2-7w-10

$$6 w ^ { 2 } - 7 w - 10$$

Tauwehe

$$\left(w-2\right)\left(6w+5\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 6w^{2}+aw+bw-10. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-7 ab=6\left(-10\right)=-60$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -60.

$$1,-60 2,-30 3,-20 4,-15 5,-12 6,-10$$

Tātaihia te tapeke mō ia takirua.

$$1-60=-59 2-30=-28 3-20=-17 4-15=-11 5-12=-7 6-10=-4$$

Ko te otinga te takirua ka hoatu i te tapeke -7.

$$a=-12 b=5$$

Tuhia anō te 6w^{2}-7w-10 hei \left(6w^{2}-12w\right)+\left(5w-10\right).

$$\left(6w^{2}-12w\right)+\left(5w-10\right)$$

Tauwehea te 6w i te tuatahi me te 5 i te rōpū tuarua.

$$6w\left(w-2\right)+5\left(w-2\right)$$

Whakatauwehea atu te kīanga pātahi w-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(w-2\right)\left(6w+5\right)$$

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.

$$6w^{2}-7w-10=0$$

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.

$$w=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 6\left(-10\right)}}{2\times 6}$$

Pūrua -7.

$$w=\frac{-\left(-7\right)±\sqrt{49-4\times 6\left(-10\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$w=\frac{-\left(-7\right)±\sqrt{49-24\left(-10\right)}}{2\times 6}$$

Whakareatia -24 ki te -10.

$$w=\frac{-\left(-7\right)±\sqrt{49+240}}{2\times 6}$$

Tāpiri 49 ki te 240.

$$w=\frac{-\left(-7\right)±\sqrt{289}}{2\times 6}$$

Tuhia te pūtakerua o te 289.

$$w=\frac{-\left(-7\right)±17}{2\times 6}$$

Ko te tauaro o -7 ko 7.

$$w=\frac{7±17}{2\times 6}$$

Whakareatia 2 ki te 6.

$$w=\frac{7±17}{12}$$

Nā, me whakaoti te whārite w=\frac{7±17}{12} ina he tāpiri te ±. Tāpiri 7 ki te 17.

$$w=\frac{24}{12}$$

Whakawehe 24 ki te 12.

$$w=2$$

Nā, me whakaoti te whārite w=\frac{7±17}{12} ina he tango te ±. Tango 17 mai i 7.

$$w=-\frac{10}{12}$$

Whakahekea te hautanga \frac{-10}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$w=-\frac{5}{6}$$

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 2 mō te x_{1} me te -\frac{5}{6} mō te x_{2}.

$$6w^{2}-7w-10=6\left(w-2\right)\left(w-\left(-\frac{5}{6}\right)\right)$$

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

$$6w^{2}-7w-10=6\left(w-2\right)\left(w+\frac{5}{6}\right)$$

Tāpiri \frac{5}{6} ki te w 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.

$$6w^{2}-7w-10=6\left(w-2\right)\times \frac{6w+5}{6}$$

Whakakorea atu te tauwehe pūnoa nui rawa 6 i roto i te 6 me te 6.

$$6w^{2}-7w-10=\left(w-2\right)\left(6w+5\right)$$

Aromātai

$$\left(w-2\right)\left(6w+5\right)$$