Whakaoti i te 16+6x-x^2

$$16 + 6 x - x ^ { 2 }$$

Tauwehe

$$-\left(x-8\right)\left(x+2\right)$$

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.

$$-x^{2}+6x+16$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -x^{2}+ax+bx+16. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=-16=-16$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -16.

$$-1,16 -2,8 -4,4$$

Tātaihia te tapeke mō ia takirua.

$$-1+16=15 -2+8=6 -4+4=0$$

Ko te otinga te takirua ka hoatu i te tapeke 6.

$$a=8 b=-2$$

Tuhia anō te -x^{2}+6x+16 hei \left(-x^{2}+8x\right)+\left(-2x+16\right).

$$\left(-x^{2}+8x\right)+\left(-2x+16\right)$$

Tauwehea te -x i te tuatahi me te -2 i te rōpū tuarua.

$$-x\left(x-8\right)-2\left(x-8\right)$$

Whakatauwehea atu te kīanga pātahi x-8 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-8\right)\left(-x-2\right)$$

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.

$$-x^{2}+6x+16=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-1\right)\times 16}}{2\left(-1\right)}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\left(-1\right)\times 16}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-6±\sqrt{36+4\times 16}}{2\left(-1\right)}$$

Whakareatia 4 ki te 16.

$$x=\frac{-6±\sqrt{36+64}}{2\left(-1\right)}$$

Tāpiri 36 ki te 64.

$$x=\frac{-6±\sqrt{100}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 100.

$$x=\frac{-6±10}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-6±10}{-2}$$

Nā, me whakaoti te whārite x=\frac{-6±10}{-2} ina he tāpiri te ±. Tāpiri -6 ki te 10.

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

Whakawehe 4 ki te -2.

$$x=-2$$

Nā, me whakaoti te whārite x=\frac{-6±10}{-2} ina he tango te ±. Tango 10 mai i -6.

$$x=-\frac{16}{-2}$$

Whakawehe -16 ki te -2.

$$x=8$$

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 -2 mō te x_{1} me te 8 mō te x_{2}.

$$-x^{2}+6x+16=-\left(x-\left(-2\right)\right)\left(x-8\right)$$

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

$$-x^{2}+6x+16=-\left(x+2\right)\left(x-8\right)$$

Aromātai

$$-\left(x-8\right)\left(x+2\right)$$