Whakaoti i te -x^2+9x-18

$$- x ^ { 2 } + 9 x - 18$$

Tauwehe

$$\left(3-x\right)\left(x-6\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -x^{2}+ax+bx-18. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=9 ab=-\left(-18\right)=18$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 18.

$$1,18 2,9 3,6$$

Tātaihia te tapeke mō ia takirua.

$$1+18=19 2+9=11 3+6=9$$

Ko te otinga te takirua ka hoatu i te tapeke 9.

$$a=6 b=3$$

Tuhia anō te -x^{2}+9x-18 hei \left(-x^{2}+6x\right)+\left(3x-18\right).

$$\left(-x^{2}+6x\right)+\left(3x-18\right)$$

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

$$-x\left(x-6\right)+3\left(x-6\right)$$

Whakatauwehea atu te kīanga pātahi x-6 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-6\right)\left(-x+3\right)$$

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.

$$-x^{2}+9x-18=0$$

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.

$$x=\frac{-9±\sqrt{9^{2}-4\left(-1\right)\left(-18\right)}}{2\left(-1\right)}$$

Pūrua 9.

$$x=\frac{-9±\sqrt{81-4\left(-1\right)\left(-18\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-9±\sqrt{81+4\left(-18\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -18.

$$x=\frac{-9±\sqrt{81-72}}{2\left(-1\right)}$$

Tāpiri 81 ki te -72.

$$x=\frac{-9±\sqrt{9}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 9.

$$x=\frac{-9±3}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-9±3}{-2}$$

Nā, me whakaoti te whārite x=\frac{-9±3}{-2} ina he tāpiri te ±. Tāpiri -9 ki te 3.

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

Whakawehe -6 ki te -2.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{-9±3}{-2} ina he tango te ±. Tango 3 mai i -9.

$$x=-\frac{12}{-2}$$

Whakawehe -12 ki te -2.

$$x=6$$

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 6 mō te x_{2}.

$$-x^{2}+9x-18=-\left(x-3\right)\left(x-6\right)$$

Aromātai

$$\left(3-x\right)\left(x-6\right)$$