Whakaoti i te 5w^2+13w-6

$$5 w ^ { 2 } + 13 w - 6$$

Tauwehe

$$\left(5w-2\right)\left(w+3\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 5w^{2}+aw+bw-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=13 ab=5\left(-6\right)=-30$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -30.

$$-1,30 -2,15 -3,10 -5,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+30=29 -2+15=13 -3+10=7 -5+6=1$$

Ko te otinga te takirua ka hoatu i te tapeke 13.

$$a=-2 b=15$$

Tuhia anō te 5w^{2}+13w-6 hei \left(5w^{2}-2w\right)+\left(15w-6\right).

$$\left(5w^{2}-2w\right)+\left(15w-6\right)$$

Tauwehea te w i te tuatahi me te 3 i te rōpū tuarua.

$$w\left(5w-2\right)+3\left(5w-2\right)$$

Whakatauwehea atu te kīanga pātahi 5w-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(5w-2\right)\left(w+3\right)$$

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.

$$5w^{2}+13w-6=0$$

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.

$$w=\frac{-13±\sqrt{13^{2}-4\times 5\left(-6\right)}}{2\times 5}$$

Pūrua 13.

$$w=\frac{-13±\sqrt{169-4\times 5\left(-6\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$w=\frac{-13±\sqrt{169-20\left(-6\right)}}{2\times 5}$$

Whakareatia -20 ki te -6.

$$w=\frac{-13±\sqrt{169+120}}{2\times 5}$$

Tāpiri 169 ki te 120.

$$w=\frac{-13±\sqrt{289}}{2\times 5}$$

Tuhia te pūtakerua o te 289.

$$w=\frac{-13±17}{2\times 5}$$

Whakareatia 2 ki te 5.

$$w=\frac{-13±17}{10}$$

Nā, me whakaoti te whārite w=\frac{-13±17}{10} ina he tāpiri te ±. Tāpiri -13 ki te 17.

$$w=\frac{4}{10}$$

Whakahekea te hautanga \frac{4}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$w=\frac{2}{5}$$

Nā, me whakaoti te whārite w=\frac{-13±17}{10} ina he tango te ±. Tango 17 mai i -13.

$$w=-\frac{30}{10}$$

Whakawehe -30 ki te 10.

$$w=-3$$

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

$$5w^{2}+13w-6=5\left(w-\frac{2}{5}\right)\left(w-\left(-3\right)\right)$$

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

$$5w^{2}+13w-6=5\left(w-\frac{2}{5}\right)\left(w+3\right)$$

Tango \frac{2}{5} mai i w 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.

$$5w^{2}+13w-6=5\times \frac{5w-2}{5}\left(w+3\right)$$

Whakakorea atu te tauwehe pūnoa nui rawa 5 i roto i te 5 me te 5.

$$5w^{2}+13w-6=\left(5w-2\right)\left(w+3\right)$$

Aromātai

$$\left(5w-2\right)\left(w+3\right)$$