Whakaoti i te 6x^2=1-x

$$6 x ^ { 2 } = 1 - x$$

Whakaoti mō x

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

$$x=\frac{1}{3}\approx 0.333333333$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 1 mai i ngā taha e rua.

$$6x^{2}-1=-x$$

Me tāpiri te x ki ngā taha e rua.

$$6x^{2}-1+x=0$$

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

$$6x^{2}+x-1=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 6x^{2}+ax+bx-1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=6\left(-1\right)=-6$$

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 -6.

$$-1,6 -2,3$$

Tātaihia te tapeke mō ia takirua.

$$-1+6=5 -2+3=1$$

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

$$a=-2 b=3$$

Tuhia anō te 6x^{2}+x-1 hei \left(6x^{2}-2x\right)+\left(3x-1\right).

$$\left(6x^{2}-2x\right)+\left(3x-1\right)$$

Whakatauwehea atu 2x i te 6x^{2}-2x.

$$2x\left(3x-1\right)+3x-1$$

Whakatauwehea atu te kīanga pātahi 3x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(3x-1\right)\left(2x+1\right)$$

Hei kimi otinga whārite, me whakaoti te 3x-1=0 me te 2x+1=0.

$$x=\frac{1}{3} x=-\frac{1}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 1 mai i ngā taha e rua.

$$6x^{2}-1=-x$$

Me tāpiri te x ki ngā taha e rua.

$$6x^{2}-1+x=0$$

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.

$$6x^{2}+x-1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 1 mō b, me -1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\times 6\left(-1\right)}}{2\times 6}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\times 6\left(-1\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-1±\sqrt{1-24\left(-1\right)}}{2\times 6}$$

Whakareatia -24 ki te -1.

$$x=\frac{-1±\sqrt{1+24}}{2\times 6}$$

Tāpiri 1 ki te 24.

$$x=\frac{-1±\sqrt{25}}{2\times 6}$$

Tuhia te pūtakerua o te 25.

$$x=\frac{-1±5}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-1±5}{12}$$

Nā, me whakaoti te whārite x=\frac{-1±5}{12} ina he tāpiri te ±. Tāpiri -1 ki te 5.

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

Whakahekea te hautanga \frac{4}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Nā, me whakaoti te whārite x=\frac{-1±5}{12} ina he tango te ±. Tango 5 mai i -1.

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

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

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

Kua oti te whārite te whakatau.

$$x=\frac{1}{3} x=-\frac{1}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te x ki ngā taha e rua.

$$6x^{2}+x=1$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}+x}{6}=\frac{1}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$x^{2}+\frac{1}{6}x=\frac{1}{6}$$

Whakawehea te \frac{1}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{12}. Nā, tāpiria te pūrua o te \frac{1}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{1}{6}x+\left(\frac{1}{12}\right)^{2}=\frac{1}{6}+\left(\frac{1}{12}\right)^{2}$$

Pūruatia \frac{1}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{1}{6}x+\frac{1}{144}=\frac{1}{6}+\frac{1}{144}$$

Tāpiri \frac{1}{6} ki te \frac{1}{144} 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.

$$x^{2}+\frac{1}{6}x+\frac{1}{144}=\frac{25}{144}$$

Tauwehea x^{2}+\frac{1}{6}x+\frac{1}{144}. 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}.

$$\left(x+\frac{1}{12}\right)^{2}=\frac{25}{144}$$

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

$$\sqrt{\left(x+\frac{1}{12}\right)^{2}}=\sqrt{\frac{25}{144}}$$

Whakarūnātia.

$$x+\frac{1}{12}=\frac{5}{12} x+\frac{1}{12}=-\frac{5}{12}$$

Me tango \frac{1}{12} mai i ngā taha e rua o te whārite.

$$x=\frac{1}{3} x=-\frac{1}{2}$$