Whakaoti i te 4x-9+12x=3/2x-2x

$$4x-9+12x= \frac{ 3 }{ 2x } -2x$$

Whakaoti mō x

$$x=\frac{\sqrt{21}}{12}+\frac{1}{4}\approx 0.631881308$$

$$x=-\frac{\sqrt{21}}{12}+\frac{1}{4}\approx -0.131881308$$

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 2x.

$$4x\times 2x+2x\left(-9\right)+12x\times 2x=3-2x\times 2x$$

Whakareatia te 4 ki te 2, ka 8.

$$8xx+2x\left(-9\right)+12x\times 2x=3-2x\times 2x$$

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

$$8x^{2}+2x\left(-9\right)+12x\times 2x=3-2x\times 2x$$

Whakareatia te 2 ki te -9, ka -18.

$$8x^{2}-18x+12x\times 2x=3-2x\times 2x$$

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

$$8x^{2}-18x+12x^{2}\times 2=3-2x\times 2x$$

Whakareatia te 12 ki te 2, ka 24.

$$8x^{2}-18x+24x^{2}=3-2x\times 2x$$

Pahekotia te 8x^{2} me 24x^{2}, ka 32x^{2}.

$$32x^{2}-18x=3-2x\times 2x$$

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

$$32x^{2}-18x=3-2x^{2}\times 2$$

Whakareatia te -2 ki te 2, ka -4.

$$32x^{2}-18x=3-4x^{2}$$

Tangohia te 3 mai i ngā taha e rua.

$$32x^{2}-18x-3=-4x^{2}$$

Me tāpiri te 4x^{2} ki ngā taha e rua.

$$32x^{2}-18x-3+4x^{2}=0$$

Pahekotia te 32x^{2} me 4x^{2}, ka 36x^{2}.

$$36x^{2}-18x-3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 36 mō a, -18 mō b, me -3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 36\left(-3\right)}}{2\times 36}$$

Pūrua -18.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 36\left(-3\right)}}{2\times 36}$$

Whakareatia -4 ki te 36.

$$x=\frac{-\left(-18\right)±\sqrt{324-144\left(-3\right)}}{2\times 36}$$

Whakareatia -144 ki te -3.

$$x=\frac{-\left(-18\right)±\sqrt{324+432}}{2\times 36}$$

Tāpiri 324 ki te 432.

$$x=\frac{-\left(-18\right)±\sqrt{756}}{2\times 36}$$

Tuhia te pūtakerua o te 756.

$$x=\frac{-\left(-18\right)±6\sqrt{21}}{2\times 36}$$

Ko te tauaro o -18 ko 18.

$$x=\frac{18±6\sqrt{21}}{2\times 36}$$

Whakareatia 2 ki te 36.

$$x=\frac{18±6\sqrt{21}}{72}$$

Nā, me whakaoti te whārite x=\frac{18±6\sqrt{21}}{72} ina he tāpiri te ±. Tāpiri 18 ki te 6\sqrt{21}.

$$x=\frac{6\sqrt{21}+18}{72}$$

Whakawehe 18+6\sqrt{21} ki te 72.

$$x=\frac{\sqrt{21}}{12}+\frac{1}{4}$$

Nā, me whakaoti te whārite x=\frac{18±6\sqrt{21}}{72} ina he tango te ±. Tango 6\sqrt{21} mai i 18.

$$x=\frac{18-6\sqrt{21}}{72}$$

Whakawehe 18-6\sqrt{21} ki te 72.

$$x=-\frac{\sqrt{21}}{12}+\frac{1}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{21}}{12}+\frac{1}{4} x=-\frac{\sqrt{21}}{12}+\frac{1}{4}$$

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 2x.

$$4x\times 2x+2x\left(-9\right)+12x\times 2x=3-2x\times 2x$$

Whakareatia te 4 ki te 2, ka 8.

$$8xx+2x\left(-9\right)+12x\times 2x=3-2x\times 2x$$

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

$$8x^{2}+2x\left(-9\right)+12x\times 2x=3-2x\times 2x$$

Whakareatia te 2 ki te -9, ka -18.

$$8x^{2}-18x+12x\times 2x=3-2x\times 2x$$

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

$$8x^{2}-18x+12x^{2}\times 2=3-2x\times 2x$$

Whakareatia te 12 ki te 2, ka 24.

$$8x^{2}-18x+24x^{2}=3-2x\times 2x$$

Pahekotia te 8x^{2} me 24x^{2}, ka 32x^{2}.

$$32x^{2}-18x=3-2x\times 2x$$

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

$$32x^{2}-18x=3-2x^{2}\times 2$$

Whakareatia te -2 ki te 2, ka -4.

$$32x^{2}-18x=3-4x^{2}$$

Me tāpiri te 4x^{2} ki ngā taha e rua.

$$32x^{2}-18x+4x^{2}=3$$

Pahekotia te 32x^{2} me 4x^{2}, ka 36x^{2}.

$$36x^{2}-18x=3$$

Whakawehea ngā taha e rua ki te 36.

$$\frac{36x^{2}-18x}{36}=\frac{3}{36}$$

Mā te whakawehe ki te 36 ka wetekia te whakareanga ki te 36.

$$x^{2}+\left(-\frac{18}{36}\right)x=\frac{3}{36}$$

Whakahekea te hautanga \frac{-18}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 18.

$$x^{2}-\frac{1}{2}x=\frac{3}{36}$$

Whakahekea te hautanga \frac{3}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

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

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.

$$x^{2}-\frac{1}{2}x+\left(-\frac{1}{4}\right)^{2}=\frac{1}{12}+\left(-\frac{1}{4}\right)^{2}$$

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

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{1}{12}+\frac{1}{16}$$

Tāpiri \frac{1}{12} 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.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{7}{48}$$

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}.

$$\left(x-\frac{1}{4}\right)^{2}=\frac{7}{48}$$

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

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{\frac{7}{48}}$$

Whakarūnātia.

$$x-\frac{1}{4}=\frac{\sqrt{21}}{12} x-\frac{1}{4}=-\frac{\sqrt{21}}{12}$$

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

$$x=\frac{\sqrt{21}}{12}+\frac{1}{4} x=-\frac{\sqrt{21}}{12}+\frac{1}{4}$$