Whakaoti i te 2x(3x-2)-4=x

$$2x(3x-2)-4=x$$

Whakaoti mō x

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

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te 3x-2.

$$6x^{2}-4x-4=x$$

Tangohia te x mai i ngā taha e rua.

$$6x^{2}-4x-4-x=0$$

Pahekotia te -4x me -x, ka -5x.

$$6x^{2}-5x-4=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 6x^{2}+ax+bx-4. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-5 ab=6\left(-4\right)=-24$$

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 -24.

$$1,-24 2,-12 3,-8 4,-6$$

Tātaihia te tapeke mō ia takirua.

$$1-24=-23 2-12=-10 3-8=-5 4-6=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -5.

$$a=-8 b=3$$

Tuhia anō te 6x^{2}-5x-4 hei \left(6x^{2}-8x\right)+\left(3x-4\right).

$$\left(6x^{2}-8x\right)+\left(3x-4\right)$$

Whakatauwehea atu 2x i te 6x^{2}-8x.

$$2x\left(3x-4\right)+3x-4$$

Whakatauwehea atu te kīanga pātahi 3x-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(3x-4\right)\left(2x+1\right)$$

Hei kimi otinga whārite, me whakaoti te 3x-4=0 me te 2x+1=0.

$$x=\frac{4}{3} x=-\frac{1}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te 3x-2.

$$6x^{2}-4x-4=x$$

Tangohia te x mai i ngā taha e rua.

$$6x^{2}-4x-4-x=0$$

Pahekotia te -4x me -x, ka -5x.

$$6x^{2}-5x-4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, -5 mō b, me -4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 6\left(-4\right)}}{2\times 6}$$

Pūrua -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 6\left(-4\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-\left(-5\right)±\sqrt{25-24\left(-4\right)}}{2\times 6}$$

Whakareatia -24 ki te -4.

$$x=\frac{-\left(-5\right)±\sqrt{25+96}}{2\times 6}$$

Tāpiri 25 ki te 96.

$$x=\frac{-\left(-5\right)±\sqrt{121}}{2\times 6}$$

Tuhia te pūtakerua o te 121.

$$x=\frac{-\left(-5\right)±11}{2\times 6}$$

Ko te tauaro o -5 ko 5.

$$x=\frac{5±11}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{5±11}{12}$$

Nā, me whakaoti te whārite x=\frac{5±11}{12} ina he tāpiri te ±. Tāpiri 5 ki te 11.

$$x=\frac{16}{12}$$

Whakahekea te hautanga \frac{16}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Nā, me whakaoti te whārite x=\frac{5±11}{12} ina he tango te ±. Tango 11 mai i 5.

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

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.

$$x=\frac{4}{3} x=-\frac{1}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te 3x-2.

$$6x^{2}-4x-4=x$$

Tangohia te x mai i ngā taha e rua.

$$6x^{2}-4x-4-x=0$$

Pahekotia te -4x me -x, ka -5x.

$$6x^{2}-5x-4=0$$

Me tāpiri te 4 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$6x^{2}-5x=4$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}-5x}{6}=\frac{4}{6}$$

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

$$x^{2}-\frac{5}{6}x=\frac{4}{6}$$

Whakahekea te hautanga \frac{4}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{5}{6}x=\frac{2}{3}$$

Whakawehea te -\frac{5}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{12}. Nā, tāpiria te pūrua o te -\frac{5}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{5}{6}x+\left(-\frac{5}{12}\right)^{2}=\frac{2}{3}+\left(-\frac{5}{12}\right)^{2}$$

Pūruatia -\frac{5}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{5}{6}x+\frac{25}{144}=\frac{2}{3}+\frac{25}{144}$$

Tāpiri \frac{2}{3} ki te \frac{25}{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.

$$x^{2}-\frac{5}{6}x+\frac{25}{144}=\frac{121}{144}$$

Tauwehea x^{2}-\frac{5}{6}x+\frac{25}{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}.

$$\left(x-\frac{5}{12}\right)^{2}=\frac{121}{144}$$

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

$$\sqrt{\left(x-\frac{5}{12}\right)^{2}}=\sqrt{\frac{121}{144}}$$

Whakarūnātia.

$$x-\frac{5}{12}=\frac{11}{12} x-\frac{5}{12}=-\frac{11}{12}$$

Me tāpiri \frac{5}{12} ki ngā taha e rua o te whārite.

$$x=\frac{4}{3} x=-\frac{1}{2}$$