Whakaoti i te x^2+5x-36

$${ x }^{ 2 } +5x-36$$

Tauwehe

$$\left(x-4\right)\left(x+9\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-36. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=1\left(-36\right)=-36$$

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 -36.

$$-1,36 -2,18 -3,12 -4,9 -6,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+36=35 -2+18=16 -3+12=9 -4+9=5 -6+6=0$$

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

$$a=-4 b=9$$

Tuhia anō te x^{2}+5x-36 hei \left(x^{2}-4x\right)+\left(9x-36\right).

$$\left(x^{2}-4x\right)+\left(9x-36\right)$$

Tauwehea te x i te tuatahi me te 9 i te rōpū tuarua.

$$x\left(x-4\right)+9\left(x-4\right)$$

Whakatauwehea atu te kīanga pātahi x-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-4\right)\left(x+9\right)$$

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.

$$x^{2}+5x-36=0$$

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.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-36\right)}}{2}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\left(-36\right)}}{2}$$

Whakareatia -4 ki te -36.

$$x=\frac{-5±\sqrt{25+144}}{2}$$

Tāpiri 25 ki te 144.

$$x=\frac{-5±\sqrt{169}}{2}$$

Tuhia te pūtakerua o te 169.

$$x=\frac{-5±13}{2}$$

Nā, me whakaoti te whārite x=\frac{-5±13}{2} ina he tāpiri te ±. Tāpiri -5 ki te 13.

$$x=\frac{8}{2}$$

Whakawehe 8 ki te 2.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{-5±13}{2} ina he tango te ±. Tango 13 mai i -5.

$$x=-\frac{18}{2}$$

Whakawehe -18 ki te 2.

$$x=-9$$

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 4 mō te x_{1} me te -9 mō te x_{2}.

$$x^{2}+5x-36=\left(x-4\right)\left(x-\left(-9\right)\right)$$

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

$$x^{2}+5x-36=\left(x-4\right)\left(x+9\right)$$

Aromātai

$$\left(x-4\right)\left(x+9\right)$$