Whakaoti i te -x^2+24+5x

$$- x ^ { 2 } + 24 + 5 x$$

Tauwehe

$$-\left(x-8\right)\left(x+3\right)$$

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.

$$-x^{2}+5x+24$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -x^{2}+ax+bx+24. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=-24=-24$$

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 -24.

$$-1,24 -2,12 -3,8 -4,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+24=23 -2+12=10 -3+8=5 -4+6=2$$

Ko te otinga te takirua ka hoatu i te tapeke 5.

$$a=8 b=-3$$

Tuhia anō te -x^{2}+5x+24 hei \left(-x^{2}+8x\right)+\left(-3x+24\right).

$$\left(-x^{2}+8x\right)+\left(-3x+24\right)$$

Tauwehea te -x i te tuatahi me te -3 i te rōpū tuarua.

$$-x\left(x-8\right)-3\left(x-8\right)$$

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

$$\left(x-8\right)\left(-x-3\right)$$

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.

$$-x^{2}+5x+24=0$$

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.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-1\right)\times 24}}{2\left(-1\right)}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\left(-1\right)\times 24}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-5±\sqrt{25+4\times 24}}{2\left(-1\right)}$$

Whakareatia 4 ki te 24.

$$x=\frac{-5±\sqrt{25+96}}{2\left(-1\right)}$$

Tāpiri 25 ki te 96.

$$x=\frac{-5±\sqrt{121}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 121.

$$x=\frac{-5±11}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-5±11}{-2}$$

Nā, me whakaoti te whārite x=\frac{-5±11}{-2} ina he tāpiri te ±. Tāpiri -5 ki te 11.

$$x=\frac{6}{-2}$$

Whakawehe 6 ki te -2.

$$x=-3$$

Nā, me whakaoti te whārite x=\frac{-5±11}{-2} ina he tango te ±. Tango 11 mai i -5.

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

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 -3 mō te x_{1} me te 8 mō te x_{2}.

$$-x^{2}+5x+24=-\left(x-\left(-3\right)\right)\left(x-8\right)$$

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

$$-x^{2}+5x+24=-\left(x+3\right)\left(x-8\right)$$

Aromātai

$$-\left(x-8\right)\left(x+3\right)$$