Whakaoti i te 2w^2+w-66

$$2 w ^ { 2 } + w - 66$$

Tauwehe

$$\left(2w-11\right)\left(w+6\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 2w^{2}+aw+bw-66. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=2\left(-66\right)=-132$$

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 -132.

$$-1,132 -2,66 -3,44 -4,33 -6,22 -11,12$$

Tātaihia te tapeke mō ia takirua.

$$-1+132=131 -2+66=64 -3+44=41 -4+33=29 -6+22=16 -11+12=1$$

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

$$a=-11 b=12$$

Tuhia anō te 2w^{2}+w-66 hei \left(2w^{2}-11w\right)+\left(12w-66\right).

$$\left(2w^{2}-11w\right)+\left(12w-66\right)$$

Tauwehea te w i te tuatahi me te 6 i te rōpū tuarua.

$$w\left(2w-11\right)+6\left(2w-11\right)$$

Whakatauwehea atu te kīanga pātahi 2w-11 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2w-11\right)\left(w+6\right)$$

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.

$$2w^{2}+w-66=0$$

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.

$$w=\frac{-1±\sqrt{1^{2}-4\times 2\left(-66\right)}}{2\times 2}$$

Pūrua 1.

$$w=\frac{-1±\sqrt{1-4\times 2\left(-66\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$w=\frac{-1±\sqrt{1-8\left(-66\right)}}{2\times 2}$$

Whakareatia -8 ki te -66.

$$w=\frac{-1±\sqrt{1+528}}{2\times 2}$$

Tāpiri 1 ki te 528.

$$w=\frac{-1±\sqrt{529}}{2\times 2}$$

Tuhia te pūtakerua o te 529.

$$w=\frac{-1±23}{2\times 2}$$

Whakareatia 2 ki te 2.

$$w=\frac{-1±23}{4}$$

Nā, me whakaoti te whārite w=\frac{-1±23}{4} ina he tāpiri te ±. Tāpiri -1 ki te 23.

$$w=\frac{22}{4}$$

Whakahekea te hautanga \frac{22}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$w=\frac{11}{2}$$

Nā, me whakaoti te whārite w=\frac{-1±23}{4} ina he tango te ±. Tango 23 mai i -1.

$$w=-\frac{24}{4}$$

Whakawehe -24 ki te 4.

$$w=-6$$

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 \frac{11}{2} mō te x_{1} me te -6 mō te x_{2}.

$$2w^{2}+w-66=2\left(w-\frac{11}{2}\right)\left(w-\left(-6\right)\right)$$

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

$$2w^{2}+w-66=2\left(w-\frac{11}{2}\right)\left(w+6\right)$$

Tango \frac{11}{2} mai i w mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$2w^{2}+w-66=2\times \frac{2w-11}{2}\left(w+6\right)$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 2 me te 2.

$$2w^{2}+w-66=\left(2w-11\right)\left(w+6\right)$$

Aromātai

$$\left(2w-11\right)\left(w+6\right)$$