Whakaoti i te 5u^2-15u-50

$$5 u ^ { 2 } - 15 u - 50$$

Tauwehe

$$5\left(u-5\right)\left(u+2\right)$$

Ngā Upane Otinga

Tauwehea te 5.

$$5\left(u^{2}-3u-10\right)$$

Whakaarohia te u^{2}-3u-10. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei u^{2}+au+bu-10. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-3 ab=1\left(-10\right)=-10$$

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 -10.

$$1,-10 2,-5$$

Tātaihia te tapeke mō ia takirua.

$$1-10=-9 2-5=-3$$

Ko te otinga te takirua ka hoatu i te tapeke -3.

$$a=-5 b=2$$

Tuhia anō te u^{2}-3u-10 hei \left(u^{2}-5u\right)+\left(2u-10\right).

$$\left(u^{2}-5u\right)+\left(2u-10\right)$$

Tauwehea te u i te tuatahi me te 2 i te rōpū tuarua.

$$u\left(u-5\right)+2\left(u-5\right)$$

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

$$\left(u-5\right)\left(u+2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$5\left(u-5\right)\left(u+2\right)$$

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.

$$5u^{2}-15u-50=0$$

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.

$$u=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 5\left(-50\right)}}{2\times 5}$$

Pūrua -15.

$$u=\frac{-\left(-15\right)±\sqrt{225-4\times 5\left(-50\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$u=\frac{-\left(-15\right)±\sqrt{225-20\left(-50\right)}}{2\times 5}$$

Whakareatia -20 ki te -50.

$$u=\frac{-\left(-15\right)±\sqrt{225+1000}}{2\times 5}$$

Tāpiri 225 ki te 1000.

$$u=\frac{-\left(-15\right)±\sqrt{1225}}{2\times 5}$$

Tuhia te pūtakerua o te 1225.

$$u=\frac{-\left(-15\right)±35}{2\times 5}$$

Ko te tauaro o -15 ko 15.

$$u=\frac{15±35}{2\times 5}$$

Whakareatia 2 ki te 5.

$$u=\frac{15±35}{10}$$

Nā, me whakaoti te whārite u=\frac{15±35}{10} ina he tāpiri te ±. Tāpiri 15 ki te 35.

$$u=\frac{50}{10}$$

Whakawehe 50 ki te 10.

$$u=5$$

Nā, me whakaoti te whārite u=\frac{15±35}{10} ina he tango te ±. Tango 35 mai i 15.

$$u=-\frac{20}{10}$$

Whakawehe -20 ki te 10.

$$u=-2$$

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 5 mō te x_{1} me te -2 mō te x_{2}.

$$5u^{2}-15u-50=5\left(u-5\right)\left(u-\left(-2\right)\right)$$

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

$$5u^{2}-15u-50=5\left(u-5\right)\left(u+2\right)$$

Aromātai

$$5\left(u-5\right)\left(u+2\right)$$