Whakaoti i te x*(x-1)=-2*(x^2+x+1)

$$x \cdot ( x - 1 ) = - 2 \cdot ( x ^ { 2 } + x + 1 )$$

Whakaoti mō x (complex solution)

$$x=\frac{-1+\sqrt{23}i}{6}\approx -0.166666667+0.799305254i$$

$$x=\frac{-\sqrt{23}i-1}{6}\approx -0.166666667-0.799305254i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-1.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x^{2}+x+1.

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

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

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

Pahekotia te x^{2} me 2x^{2}, ka 3x^{2}.

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

Me tāpiri te 2x ki ngā taha e rua.

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

Pahekotia te -x me 2x, ka x.

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

Me tāpiri te 2 ki ngā taha e rua.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 1 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1±\sqrt{1^{2}-4\times 3\times 2}}{2\times 3}$$

Pūrua 1.

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

Whakareatia -4 ki te 3.

$$x=\frac{-1±\sqrt{1-12\times 2}}{2\times 3}$$

Whakareatia -12 ki te 2.

$$x=\frac{-1±\sqrt{1-24}}{2\times 3}$$

Tāpiri 1 ki te -24.

$$x=\frac{-1±\sqrt{-23}}{2\times 3}$$

Tuhia te pūtakerua o te -23.

$$x=\frac{-1±\sqrt{23}i}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-1±\sqrt{23}i}{6}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{23}i}{6} ina he tāpiri te ±. Tāpiri -1 ki te i\sqrt{23}.

$$x=\frac{-1+\sqrt{23}i}{6}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{23}i}{6} ina he tango te ±. Tango i\sqrt{23} mai i -1.

$$x=\frac{-\sqrt{23}i-1}{6}$$

Kua oti te whārite te whakatau.

$$x=\frac{-1+\sqrt{23}i}{6} x=\frac{-\sqrt{23}i-1}{6}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-1.

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

Whakamahia te āhuatanga tohatoha hei whakarea te -2 ki te x^{2}+x+1.

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

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

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

Pahekotia te x^{2} me 2x^{2}, ka 3x^{2}.

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

Me tāpiri te 2x ki ngā taha e rua.

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

Pahekotia te -x me 2x, ka x.

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

Whakawehea ngā taha e rua ki te 3.

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

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

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

Whakawehea te \frac{1}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{6}. Nā, tāpiria te pūrua o te \frac{1}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia \frac{1}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

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

Tāpiri -\frac{2}{3} ki te \frac{1}{36} 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.

$$x^{2}+\frac{1}{3}x+\frac{1}{36}=-\frac{23}{36}$$

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

$$\left(x+\frac{1}{6}\right)^{2}=-\frac{23}{36}$$

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

$$\sqrt{\left(x+\frac{1}{6}\right)^{2}}=\sqrt{-\frac{23}{36}}$$

Whakarūnātia.

$$x+\frac{1}{6}=\frac{\sqrt{23}i}{6} x+\frac{1}{6}=-\frac{\sqrt{23}i}{6}$$

Me tango \frac{1}{6} mai i ngā taha e rua o te whārite.

$$x=\frac{-1+\sqrt{23}i}{6} x=\frac{-\sqrt{23}i-1}{6}$$