Whakaoti i te 3x(x-1)=2-2x

$$3 x ( x - 1 ) = 2 - 2 x$$

Whakaoti mō x

$$x=-\frac{2}{3}\approx -0.666666667$$

$$x=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x-1.

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

Tangohia te 2 mai i ngā taha e rua.

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

Me tāpiri te 2x ki ngā taha e rua.

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

Pahekotia te -3x me 2x, ka -x.

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

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}.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 3\left(-2\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-1\right)±\sqrt{1-12\left(-2\right)}}{2\times 3}$$

Whakareatia -12 ki te -2.

$$x=\frac{-\left(-1\right)±\sqrt{1+24}}{2\times 3}$$

Tāpiri 1 ki te 24.

$$x=\frac{-\left(-1\right)±\sqrt{25}}{2\times 3}$$

Tuhia te pūtakerua o te 25.

$$x=\frac{-\left(-1\right)±5}{2\times 3}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±5}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{1±5}{6}$$

Nā, me whakaoti te whārite x=\frac{1±5}{6} ina he tāpiri te ±. Tāpiri 1 ki te 5.

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

Whakawehe 6 ki te 6.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{1±5}{6} ina he tango te ±. Tango 5 mai i 1.

$$x=-\frac{4}{6}$$

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

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

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te x-1.

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

Me tāpiri te 2x ki ngā taha e rua.

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

Pahekotia te -3x 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.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=\frac{25}{36}$$

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}.

$$\left(x-\frac{1}{6}\right)^{2}=\frac{25}{36}$$

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

$$\sqrt{\left(x-\frac{1}{6}\right)^{2}}=\sqrt{\frac{25}{36}}$$

Whakarūnātia.

$$x-\frac{1}{6}=\frac{5}{6} x-\frac{1}{6}=-\frac{5}{6}$$

Me tāpiri \frac{1}{6} ki ngā taha e rua o te whārite.

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