Whakaoti i te -x^2-2x+35

$$- x ^ { 2 } - 2 x + 35$$

Tauwehe

$$\left(5-x\right)\left(x+7\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -x^{2}+ax+bx+35. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-2 ab=-35=-35$$

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 -35.

$$1,-35 5,-7$$

Tātaihia te tapeke mō ia takirua.

$$1-35=-34 5-7=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -2.

$$a=5 b=-7$$

Tuhia anō te -x^{2}-2x+35 hei \left(-x^{2}+5x\right)+\left(-7x+35\right).

$$\left(-x^{2}+5x\right)+\left(-7x+35\right)$$

Tauwehea te x i te tuatahi me te 7 i te rōpū tuarua.

$$x\left(-x+5\right)+7\left(-x+5\right)$$

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

$$\left(-x+5\right)\left(x+7\right)$$

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.

$$-x^{2}-2x+35=0$$

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.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-1\right)\times 35}}{2\left(-1\right)}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-1\right)\times 35}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-2\right)±\sqrt{4+4\times 35}}{2\left(-1\right)}$$

Whakareatia 4 ki te 35.

$$x=\frac{-\left(-2\right)±\sqrt{4+140}}{2\left(-1\right)}$$

Tāpiri 4 ki te 140.

$$x=\frac{-\left(-2\right)±\sqrt{144}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 144.

$$x=\frac{-\left(-2\right)±12}{2\left(-1\right)}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±12}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{2±12}{-2}$$

Nā, me whakaoti te whārite x=\frac{2±12}{-2} ina he tāpiri te ±. Tāpiri 2 ki te 12.

$$x=\frac{14}{-2}$$

Whakawehe 14 ki te -2.

$$x=-7$$

Nā, me whakaoti te whārite x=\frac{2±12}{-2} ina he tango te ±. Tango 12 mai i 2.

$$x=-\frac{10}{-2}$$

Whakawehe -10 ki te -2.

$$x=5$$

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 5 mō te x_{2}.

$$-x^{2}-2x+35=-\left(x-\left(-7\right)\right)\left(x-5\right)$$

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

$$-x^{2}-2x+35=-\left(x+7\right)\left(x-5\right)$$

Aromātai

$$\left(5-x\right)\left(x+7\right)$$