Whakaoti i te -3x^2=-11x+12

$$- 3 x ^ { 2 } = - 11 x + 12$$

Whakaoti mō x (complex solution)

$$x=\frac{-\sqrt{23}i+11}{6}\approx 1.833333333-0.799305254i$$

$$x=\frac{11+\sqrt{23}i}{6}\approx 1.833333333+0.799305254i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 11x ki ngā taha e rua.

$$-3x^{2}+11x=12$$

Tangohia te 12 mai i ngā taha e rua.

$$-3x^{2}+11x-12=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, 11 mō b, me -12 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-11±\sqrt{11^{2}-4\left(-3\right)\left(-12\right)}}{2\left(-3\right)}$$

Pūrua 11.

$$x=\frac{-11±\sqrt{121-4\left(-3\right)\left(-12\right)}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{-11±\sqrt{121+12\left(-12\right)}}{2\left(-3\right)}$$

Whakareatia 12 ki te -12.

$$x=\frac{-11±\sqrt{121-144}}{2\left(-3\right)}$$

Tāpiri 121 ki te -144.

$$x=\frac{-11±\sqrt{-23}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te -23.

$$x=\frac{-11±\sqrt{23}i}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{-11±\sqrt{23}i}{-6}$$

Nā, me whakaoti te whārite x=\frac{-11±\sqrt{23}i}{-6} ina he tāpiri te ±. Tāpiri -11 ki te i\sqrt{23}.

$$x=\frac{-11+\sqrt{23}i}{-6}$$

Whakawehe -11+i\sqrt{23} ki te -6.

$$x=\frac{-\sqrt{23}i+11}{6}$$

Nā, me whakaoti te whārite x=\frac{-11±\sqrt{23}i}{-6} ina he tango te ±. Tango i\sqrt{23} mai i -11.

$$x=\frac{-\sqrt{23}i-11}{-6}$$

Whakawehe -11-i\sqrt{23} ki te -6.

$$x=\frac{11+\sqrt{23}i}{6}$$

Kua oti te whārite te whakatau.

$$x=\frac{-\sqrt{23}i+11}{6} x=\frac{11+\sqrt{23}i}{6}$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 11x ki ngā taha e rua.

$$-3x^{2}+11x=12$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3x^{2}+11x}{-3}=\frac{12}{-3}$$

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

$$x^{2}+\frac{11}{-3}x=\frac{12}{-3}$$

Whakawehe 11 ki te -3.

$$x^{2}-\frac{11}{3}x=\frac{12}{-3}$$

Whakawehe 12 ki te -3.

$$x^{2}-\frac{11}{3}x=-4$$

Whakawehea te -\frac{11}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{11}{6}. Nā, tāpiria te pūrua o te -\frac{11}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{11}{3}x+\left(-\frac{11}{6}\right)^{2}=-4+\left(-\frac{11}{6}\right)^{2}$$

Pūruatia -\frac{11}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{11}{3}x+\frac{121}{36}=-4+\frac{121}{36}$$

Tāpiri -4 ki te \frac{121}{36}.

$$x^{2}-\frac{11}{3}x+\frac{121}{36}=-\frac{23}{36}$$

Tauwehea x^{2}-\frac{11}{3}x+\frac{121}{36}. 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}.

$$\left(x-\frac{11}{6}\right)^{2}=-\frac{23}{36}$$

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

$$\sqrt{\left(x-\frac{11}{6}\right)^{2}}=\sqrt{-\frac{23}{36}}$$

Whakarūnātia.

$$x-\frac{11}{6}=\frac{\sqrt{23}i}{6} x-\frac{11}{6}=-\frac{\sqrt{23}i}{6}$$

Me tāpiri \frac{11}{6} ki ngā taha e rua o te whārite.

$$x=\frac{11+\sqrt{23}i}{6} x=\frac{-\sqrt{23}i+11}{6}$$