Whakaoti i te n^2-28-12n

$$n ^ { 2 } - 28 - 12 n$$

Tauwehe

$$\left(n-14\right)\left(n+2\right)$$

Ngā Upane Otinga

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$n^{2}-12n-28$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei n^{2}+an+bn-28. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-12 ab=1\left(-28\right)=-28$$

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 -28.

$$1,-28 2,-14 4,-7$$

Tātaihia te tapeke mō ia takirua.

$$1-28=-27 2-14=-12 4-7=-3$$

Ko te otinga te takirua ka hoatu i te tapeke -12.

$$a=-14 b=2$$

Tuhia anō te n^{2}-12n-28 hei \left(n^{2}-14n\right)+\left(2n-28\right).

$$\left(n^{2}-14n\right)+\left(2n-28\right)$$

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

$$n\left(n-14\right)+2\left(n-14\right)$$

Whakatauwehea atu te kīanga pātahi n-14 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(n-14\right)\left(n+2\right)$$

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.

$$n^{2}-12n-28=0$$

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.

$$n=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-28\right)}}{2}$$

Pūrua -12.

$$n=\frac{-\left(-12\right)±\sqrt{144-4\left(-28\right)}}{2}$$

Whakareatia -4 ki te -28.

$$n=\frac{-\left(-12\right)±\sqrt{144+112}}{2}$$

Tāpiri 144 ki te 112.

$$n=\frac{-\left(-12\right)±\sqrt{256}}{2}$$

Tuhia te pūtakerua o te 256.

$$n=\frac{-\left(-12\right)±16}{2}$$

Ko te tauaro o -12 ko 12.

$$n=\frac{12±16}{2}$$

Nā, me whakaoti te whārite n=\frac{12±16}{2} ina he tāpiri te ±. Tāpiri 12 ki te 16.

$$n=\frac{28}{2}$$

Whakawehe 28 ki te 2.

$$n=14$$

Nā, me whakaoti te whārite n=\frac{12±16}{2} ina he tango te ±. Tango 16 mai i 12.

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

Whakawehe -4 ki te 2.

$$n=-2$$

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 14 mō te x_{1} me te -2 mō te x_{2}.

$$n^{2}-12n-28=\left(n-14\right)\left(n-\left(-2\right)\right)$$

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

$$n^{2}-12n-28=\left(n-14\right)\left(n+2\right)$$

Aromātai

$$\left(n-14\right)\left(n+2\right)$$