Whakaoti i te 12x-6/x=6

$$12 x - \frac { 6 } { x } = 6$$

Whakaoti mō x

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

$$x=1$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$12xx-6=6x$$

Whakareatia te x ki te x, ka x^{2}.

$$12x^{2}-6=6x$$

Tangohia te 6x mai i ngā taha e rua.

$$12x^{2}-6-6x=0$$

Whakawehea ngā taha e rua ki te 6.

$$2x^{2}-1-x=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$2x^{2}-x-1=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 2x^{2}+ax+bx-1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

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

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-2 b=1$$

Tuhia anō te 2x^{2}-x-1 hei \left(2x^{2}-2x\right)+\left(x-1\right).

$$\left(2x^{2}-2x\right)+\left(x-1\right)$$

Whakatauwehea atu 2x i te 2x^{2}-2x.

$$2x\left(x-1\right)+x-1$$

Whakatauwehea atu te kīanga pātahi x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-1\right)\left(2x+1\right)$$

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

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$12xx-6=6x$$

Whakareatia te x ki te x, ka x^{2}.

$$12x^{2}-6=6x$$

Tangohia te 6x mai i ngā taha e rua.

$$12x^{2}-6-6x=0$$

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.

$$12x^{2}-6x-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 12 mō a, -6 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 12\left(-6\right)}}{2\times 12}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 12\left(-6\right)}}{2\times 12}$$

Whakareatia -4 ki te 12.

$$x=\frac{-\left(-6\right)±\sqrt{36-48\left(-6\right)}}{2\times 12}$$

Whakareatia -48 ki te -6.

$$x=\frac{-\left(-6\right)±\sqrt{36+288}}{2\times 12}$$

Tāpiri 36 ki te 288.

$$x=\frac{-\left(-6\right)±\sqrt{324}}{2\times 12}$$

Tuhia te pūtakerua o te 324.

$$x=\frac{-\left(-6\right)±18}{2\times 12}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±18}{2\times 12}$$

Whakareatia 2 ki te 12.

$$x=\frac{6±18}{24}$$

Nā, me whakaoti te whārite x=\frac{6±18}{24} ina he tāpiri te ±. Tāpiri 6 ki te 18.

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

Whakawehe 24 ki te 24.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{6±18}{24} ina he tango te ±. Tango 18 mai i 6.

$$x=-\frac{12}{24}$$

Whakahekea te hautanga \frac{-12}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

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

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$12xx-6=6x$$

Whakareatia te x ki te x, ka x^{2}.

$$12x^{2}-6=6x$$

Tangohia te 6x mai i ngā taha e rua.

$$12x^{2}-6-6x=0$$

Me tāpiri te 6 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$12x^{2}-6x=6$$

Whakawehea ngā taha e rua ki te 12.

$$\frac{12x^{2}-6x}{12}=\frac{6}{12}$$

Mā te whakawehe ki te 12 ka wetekia te whakareanga ki te 12.

$$x^{2}+\left(-\frac{6}{12}\right)x=\frac{6}{12}$$

Whakahekea te hautanga \frac{-6}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x^{2}-\frac{1}{2}x=\frac{6}{12}$$

Whakahekea te hautanga \frac{6}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x^{2}-\frac{1}{2}x=\frac{1}{2}$$

Whakawehea te -\frac{1}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{4}. Nā, tāpiria te pūrua o te -\frac{1}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia -\frac{1}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{1}{2}+\frac{1}{16}$$

Tāpiri \frac{1}{2} ki te \frac{1}{16} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{9}{16}$$

Tauwehea x^{2}-\frac{1}{2}x+\frac{1}{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}.

$$\left(x-\frac{1}{4}\right)^{2}=\frac{9}{16}$$

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

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{\frac{9}{16}}$$

Whakarūnātia.

$$x-\frac{1}{4}=\frac{3}{4} x-\frac{1}{4}=-\frac{3}{4}$$

Me tāpiri \frac{1}{4} ki ngā taha e rua o te whārite.

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