Whakaoti i te 2w^2-11w=6

$$2 w ^ { 2 } - 11 w = 6$$

Whakaoti mō w

$$w=-\frac{1}{2}=-0.5$$

$$w=6$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 6 mai i ngā taha e rua.

$$2w^{2}-11w-6=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 2w^{2}+aw+bw-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-11 ab=2\left(-6\right)=-12$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -12.

$$1,-12 2,-6 3,-4$$

Tātaihia te tapeke mō ia takirua.

$$1-12=-11 2-6=-4 3-4=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -11.

$$a=-12 b=1$$

Tuhia anō te 2w^{2}-11w-6 hei \left(2w^{2}-12w\right)+\left(w-6\right).

$$\left(2w^{2}-12w\right)+\left(w-6\right)$$

Whakatauwehea atu 2w i te 2w^{2}-12w.

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

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

$$\left(w-6\right)\left(2w+1\right)$$

Hei kimi otinga whārite, me whakaoti te w-6=0 me te 2w+1=0.

$$w=6 w=-\frac{1}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$2w^{2}-11w=6$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$2w^{2}-11w-6=6-6$$

Mā te tango i te 6 i a ia ake anō ka toe ko te 0.

$$2w^{2}-11w-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -11 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 2\left(-6\right)}}{2\times 2}$$

Pūrua -11.

$$w=\frac{-\left(-11\right)±\sqrt{121-4\times 2\left(-6\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$w=\frac{-\left(-11\right)±\sqrt{121-8\left(-6\right)}}{2\times 2}$$

Whakareatia -8 ki te -6.

$$w=\frac{-\left(-11\right)±\sqrt{121+48}}{2\times 2}$$

Tāpiri 121 ki te 48.

$$w=\frac{-\left(-11\right)±\sqrt{169}}{2\times 2}$$

Tuhia te pūtakerua o te 169.

$$w=\frac{-\left(-11\right)±13}{2\times 2}$$

Ko te tauaro o -11 ko 11.

$$w=\frac{11±13}{2\times 2}$$

Whakareatia 2 ki te 2.

$$w=\frac{11±13}{4}$$

Nā, me whakaoti te whārite w=\frac{11±13}{4} ina he tāpiri te ±. Tāpiri 11 ki te 13.

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

Whakawehe 24 ki te 4.

$$w=6$$

Nā, me whakaoti te whārite w=\frac{11±13}{4} ina he tango te ±. Tango 13 mai i 11.

$$w=-\frac{2}{4}$$

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

$$w=-\frac{1}{2}$$

Kua oti te whārite te whakatau.

$$w=6 w=-\frac{1}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$2w^{2}-11w=6$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2w^{2}-11w}{2}=\frac{6}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$w^{2}-\frac{11}{2}w=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$w^{2}-\frac{11}{2}w=3$$

Whakawehea te -\frac{11}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{11}{4}. Nā, tāpiria te pūrua o te -\frac{11}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$w^{2}-\frac{11}{2}w+\left(-\frac{11}{4}\right)^{2}=3+\left(-\frac{11}{4}\right)^{2}$$

Pūruatia -\frac{11}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$w^{2}-\frac{11}{2}w+\frac{121}{16}=3+\frac{121}{16}$$

Tāpiri 3 ki te \frac{121}{16}.

$$w^{2}-\frac{11}{2}w+\frac{121}{16}=\frac{169}{16}$$

Tauwehea w^{2}-\frac{11}{2}w+\frac{121}{16}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(w-\frac{11}{4}\right)^{2}=\frac{169}{16}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(w-\frac{11}{4}\right)^{2}}=\sqrt{\frac{169}{16}}$$

Whakarūnātia.

$$w-\frac{11}{4}=\frac{13}{4} w-\frac{11}{4}=-\frac{13}{4}$$

Me tāpiri \frac{11}{4} ki ngā taha e rua o te whārite.

$$w=6 w=-\frac{1}{2}$$