Whakaoti i te 2s^2-13s-7

$$2 s ^ { 2 } - 13 s - 7$$

Tauwehe

$$\left(s-7\right)\left(2s+1\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 2s^{2}+as+bs-7. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-13 ab=2\left(-7\right)=-14$$

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 -14.

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

Tātaihia te tapeke mō ia takirua.

$$1-14=-13 2-7=-5$$

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

$$a=-14 b=1$$

Tuhia anō te 2s^{2}-13s-7 hei \left(2s^{2}-14s\right)+\left(s-7\right).

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

Whakatauwehea atu 2s i te 2s^{2}-14s.

$$2s\left(s-7\right)+s-7$$

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

$$\left(s-7\right)\left(2s+1\right)$$

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.

$$2s^{2}-13s-7=0$$

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.

$$s=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 2\left(-7\right)}}{2\times 2}$$

Pūrua -13.

$$s=\frac{-\left(-13\right)±\sqrt{169-4\times 2\left(-7\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$s=\frac{-\left(-13\right)±\sqrt{169-8\left(-7\right)}}{2\times 2}$$

Whakareatia -8 ki te -7.

$$s=\frac{-\left(-13\right)±\sqrt{169+56}}{2\times 2}$$

Tāpiri 169 ki te 56.

$$s=\frac{-\left(-13\right)±\sqrt{225}}{2\times 2}$$

Tuhia te pūtakerua o te 225.

$$s=\frac{-\left(-13\right)±15}{2\times 2}$$

Ko te tauaro o -13 ko 13.

$$s=\frac{13±15}{2\times 2}$$

Whakareatia 2 ki te 2.

$$s=\frac{13±15}{4}$$

Nā, me whakaoti te whārite s=\frac{13±15}{4} ina he tāpiri te ±. Tāpiri 13 ki te 15.

$$s=\frac{28}{4}$$

Whakawehe 28 ki te 4.

$$s=7$$

Nā, me whakaoti te whārite s=\frac{13±15}{4} ina he tango te ±. Tango 15 mai i 13.

$$s=-\frac{2}{4}$$

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

$$s=-\frac{1}{2}$$

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 -\frac{1}{2} mō te x_{2}.

$$2s^{2}-13s-7=2\left(s-7\right)\left(s-\left(-\frac{1}{2}\right)\right)$$

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

$$2s^{2}-13s-7=2\left(s-7\right)\left(s+\frac{1}{2}\right)$$

Tāpiri \frac{1}{2} ki te s 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.

$$2s^{2}-13s-7=2\left(s-7\right)\times \frac{2s+1}{2}$$

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

$$2s^{2}-13s-7=\left(s-7\right)\left(2s+1\right)$$

Aromātai

$$\left(s-7\right)\left(2s+1\right)$$