Whakaoti i te 28+27x-x^2

$$28+27x- { x }^{ 2 }$$

Tauwehe

$$-\left(x-28\right)\left(x+1\right)$$

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.

$$-x^{2}+27x+28$$

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

$$a+b=27 ab=-28=-28$$

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 -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 27.

$$a=28 b=-1$$

Tuhia anō te -x^{2}+27x+28 hei \left(-x^{2}+28x\right)+\left(-x+28\right).

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

Tauwehea te -x i te tuatahi me te -1 i te rōpū tuarua.

$$-x\left(x-28\right)-\left(x-28\right)$$

Whakatauwehea atu te kīanga pātahi x-28 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-28\right)\left(-x-1\right)$$

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.

$$-x^{2}+27x+28=0$$

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.

$$x=\frac{-27±\sqrt{27^{2}-4\left(-1\right)\times 28}}{2\left(-1\right)}$$

Pūrua 27.

$$x=\frac{-27±\sqrt{729-4\left(-1\right)\times 28}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-27±\sqrt{729+4\times 28}}{2\left(-1\right)}$$

Whakareatia 4 ki te 28.

$$x=\frac{-27±\sqrt{729+112}}{2\left(-1\right)}$$

Tāpiri 729 ki te 112.

$$x=\frac{-27±\sqrt{841}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 841.

$$x=\frac{-27±29}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-27±29}{-2}$$

Nā, me whakaoti te whārite x=\frac{-27±29}{-2} ina he tāpiri te ±. Tāpiri -27 ki te 29.

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

Whakawehe 2 ki te -2.

$$x=-1$$

Nā, me whakaoti te whārite x=\frac{-27±29}{-2} ina he tango te ±. Tango 29 mai i -27.

$$x=-\frac{56}{-2}$$

Whakawehe -56 ki te -2.

$$x=28$$

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 28 mō te x_{2}.

$$-x^{2}+27x+28=-\left(x-\left(-1\right)\right)\left(x-28\right)$$

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

$$-x^{2}+27x+28=-\left(x+1\right)\left(x-28\right)$$

Aromātai

$$-\left(x-28\right)\left(x+1\right)$$