Whakaoti i te 2x^2-18x+36=

$$2 x ^ { 2 } - 18 x + 36 =$$

Tauwehe

$$2\left(x-6\right)\left(x-3\right)$$

Ngā Upane Otinga

Tauwehea te 2.

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

Whakaarohia te x^{2}-9x+18. 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.

$$a+b=-9 ab=1\times 18=18$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro 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.

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(x-6\right)\left(x-3\right)$$

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.

$$2x^{2}-18x+36=0$$

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.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 2\times 36}}{2\times 2}$$

Pūrua -18.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 2\times 36}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-18\right)±\sqrt{324-8\times 36}}{2\times 2}$$

Whakareatia -8 ki te 36.

$$x=\frac{-\left(-18\right)±\sqrt{324-288}}{2\times 2}$$

Tāpiri 324 ki te -288.

$$x=\frac{-\left(-18\right)±\sqrt{36}}{2\times 2}$$

Tuhia te pūtakerua o te 36.

$$x=\frac{-\left(-18\right)±6}{2\times 2}$$

Ko te tauaro o -18 ko 18.

$$x=\frac{18±6}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{18±6}{4}$$

Nā, me whakaoti te whārite x=\frac{18±6}{4} ina he tāpiri te ±. Tāpiri 18 ki te 6.

$$x=\frac{24}{4}$$

Whakawehe 24 ki te 4.

$$x=6$$

Nā, me whakaoti te whārite x=\frac{18±6}{4} ina he tango te ±. Tango 6 mai i 18.

$$x=\frac{12}{4}$$

Whakawehe 12 ki te 4.

$$x=3$$

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 6 mō te x_{1} me te 3 mō te x_{2}.

$$2x^{2}-18x+36=2\left(x-6\right)\left(x-3\right)$$

Aromātai

$$2\left(x-6\right)\left(x-3\right)$$