Whakaoti i te 2x-3xx=9

$$2x-3xx=9$$

Whakaoti mō x (complex solution)

$$x=\frac{-\sqrt{26}i+1}{3}\approx 0.333333333-1.699673171i$$

$$x=\frac{1+\sqrt{26}i}{3}\approx 0.333333333+1.699673171i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$2x-3x^{2}=9$$

Tangohia te 9 mai i ngā taha e rua.

$$2x-3x^{2}-9=0$$

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.

$$-3x^{2}+2x-9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, 2 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-3\right)\left(-9\right)}}{2\left(-3\right)}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\left(-3\right)\left(-9\right)}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{-2±\sqrt{4+12\left(-9\right)}}{2\left(-3\right)}$$

Whakareatia 12 ki te -9.

$$x=\frac{-2±\sqrt{4-108}}{2\left(-3\right)}$$

Tāpiri 4 ki te -108.

$$x=\frac{-2±\sqrt{-104}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te -104.

$$x=\frac{-2±2\sqrt{26}i}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{-2±2\sqrt{26}i}{-6}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{26}i}{-6} ina he tāpiri te ±. Tāpiri -2 ki te 2i\sqrt{26}.

$$x=\frac{-2+2\sqrt{26}i}{-6}$$

Whakawehe -2+2i\sqrt{26} ki te -6.

$$x=\frac{-\sqrt{26}i+1}{3}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{26}i}{-6} ina he tango te ±. Tango 2i\sqrt{26} mai i -2.

$$x=\frac{-2\sqrt{26}i-2}{-6}$$

Whakawehe -2-2i\sqrt{26} ki te -6.

$$x=\frac{1+\sqrt{26}i}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{-\sqrt{26}i+1}{3} x=\frac{1+\sqrt{26}i}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$2x-3x^{2}=9$$

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.

$$-3x^{2}+2x=9$$

Whakawehea ngā taha e rua ki te -3.

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

Mā te whakawehe ki te -3 ka wetekia te whakareanga ki te -3.

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

Whakawehe 2 ki te -3.

$$x^{2}-\frac{2}{3}x=\frac{9}{-3}$$

Whakawehe 9 ki te -3.

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

Whakawehea te -\frac{2}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{3}. Nā, tāpiria te pūrua o te -\frac{1}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia -\frac{1}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}=-3+\frac{1}{9}$$

Tāpiri -3 ki te \frac{1}{9}.

$$x^{2}-\frac{2}{3}x+\frac{1}{9}=-\frac{26}{9}$$

Tauwehea x^{2}-\frac{2}{3}x+\frac{1}{9}. 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}.

$$\left(x-\frac{1}{3}\right)^{2}=-\frac{26}{9}$$

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

$$\sqrt{\left(x-\frac{1}{3}\right)^{2}}=\sqrt{-\frac{26}{9}}$$

Whakarūnātia.

$$x-\frac{1}{3}=\frac{\sqrt{26}i}{3} x-\frac{1}{3}=-\frac{\sqrt{26}i}{3}$$

Me tāpiri \frac{1}{3} ki ngā taha e rua o te whārite.

$$x=\frac{1+\sqrt{26}i}{3} x=\frac{-\sqrt{26}i+1}{3}$$