Whakaoti i te 5s^2+55s+50

$$5 s ^ { 2 } + 55 s + 50$$

Tauwehe

$$5\left(s+1\right)\left(s+10\right)$$

Ngā Upane Otinga

Tauwehea te 5.

$$5\left(s^{2}+11s+10\right)$$

Whakaarohia te s^{2}+11s+10. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei s^{2}+as+bs+10. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=11 ab=1\times 10=10$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 10.

$$1,10 2,5$$

Tātaihia te tapeke mō ia takirua.

$$1+10=11 2+5=7$$

Ko te otinga te takirua ka hoatu i te tapeke 11.

$$a=1 b=10$$

Tuhia anō te s^{2}+11s+10 hei \left(s^{2}+s\right)+\left(10s+10\right).

$$\left(s^{2}+s\right)+\left(10s+10\right)$$

Tauwehea te s i te tuatahi me te 10 i te rōpū tuarua.

$$s\left(s+1\right)+10\left(s+1\right)$$

Whakatauwehea atu te kīanga pātahi s+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(s+1\right)\left(s+10\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$5\left(s+1\right)\left(s+10\right)$$

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.

$$5s^{2}+55s+50=0$$

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.

$$s=\frac{-55±\sqrt{55^{2}-4\times 5\times 50}}{2\times 5}$$

Pūrua 55.

$$s=\frac{-55±\sqrt{3025-4\times 5\times 50}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$s=\frac{-55±\sqrt{3025-20\times 50}}{2\times 5}$$

Whakareatia -20 ki te 50.

$$s=\frac{-55±\sqrt{3025-1000}}{2\times 5}$$

Tāpiri 3025 ki te -1000.

$$s=\frac{-55±\sqrt{2025}}{2\times 5}$$

Tuhia te pūtakerua o te 2025.

$$s=\frac{-55±45}{2\times 5}$$

Whakareatia 2 ki te 5.

$$s=\frac{-55±45}{10}$$

Nā, me whakaoti te whārite s=\frac{-55±45}{10} ina he tāpiri te ±. Tāpiri -55 ki te 45.

$$s=-\frac{10}{10}$$

Whakawehe -10 ki te 10.

$$s=-1$$

Nā, me whakaoti te whārite s=\frac{-55±45}{10} ina he tango te ±. Tango 45 mai i -55.

$$s=-\frac{100}{10}$$

Whakawehe -100 ki te 10.

$$s=-10$$

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 -1 mō te x_{1} me te -10 mō te x_{2}.

$$5s^{2}+55s+50=5\left(s-\left(-1\right)\right)\left(s-\left(-10\right)\right)$$

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

$$5s^{2}+55s+50=5\left(s+1\right)\left(s+10\right)$$

Aromātai

$$5\left(s+1\right)\left(s+10\right)$$