Whakaoti i te x^2+x-306

$${ x }^{ 2 } +x-306$$

Tauwehe

$$\left(x-17\right)\left(x+18\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-306. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=1\left(-306\right)=-306$$

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 -306.

$$-1,306 -2,153 -3,102 -6,51 -9,34 -17,18$$

Tātaihia te tapeke mō ia takirua.

$$-1+306=305 -2+153=151 -3+102=99 -6+51=45 -9+34=25 -17+18=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=-17 b=18$$

Tuhia anō te x^{2}+x-306 hei \left(x^{2}-17x\right)+\left(18x-306\right).

$$\left(x^{2}-17x\right)+\left(18x-306\right)$$

Tauwehea te x i te tuatahi me te 18 i te rōpū tuarua.

$$x\left(x-17\right)+18\left(x-17\right)$$

Whakatauwehea atu te kīanga pātahi x-17 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-17\right)\left(x+18\right)$$

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.

$$x^{2}+x-306=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-306\right)}}{2}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\left(-306\right)}}{2}$$

Whakareatia -4 ki te -306.

$$x=\frac{-1±\sqrt{1+1224}}{2}$$

Tāpiri 1 ki te 1224.

$$x=\frac{-1±\sqrt{1225}}{2}$$

Tuhia te pūtakerua o te 1225.

$$x=\frac{-1±35}{2}$$

Nā, me whakaoti te whārite x=\frac{-1±35}{2} ina he tāpiri te ±. Tāpiri -1 ki te 35.

$$x=\frac{34}{2}$$

Whakawehe 34 ki te 2.

$$x=17$$

Nā, me whakaoti te whārite x=\frac{-1±35}{2} ina he tango te ±. Tango 35 mai i -1.

$$x=-\frac{36}{2}$$

Whakawehe -36 ki te 2.

$$x=-18$$

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 17 mō te x_{1} me te -18 mō te x_{2}.

$$x^{2}+x-306=\left(x-17\right)\left(x-\left(-18\right)\right)$$

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

$$x^{2}+x-306=\left(x-17\right)\left(x+18\right)$$

Aromātai

$$\left(x-17\right)\left(x+18\right)$$