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

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

Whakaoti mō x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-1.

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

Tangohia te 2x^{2} mai i ngā taha e rua.

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

Me tāpiri te 2x ki ngā taha e rua.

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

Pahekotia te x me 2x, ka 3x.

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

Tauwehea te x.

$$x\left(3-2x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 3-2x=0.

$$x=0 x=\frac{3}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-1.

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

Tangohia te 2x^{2} mai i ngā taha e rua.

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

Me tāpiri te 2x ki ngā taha e rua.

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

Pahekotia te x me 2x, ka 3x.

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

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.

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

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

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

Tuhia te pūtakerua o te 3^{2}.

$$x=\frac{-3±3}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-3±3}{-4}$$

Nā, me whakaoti te whārite x=\frac{-3±3}{-4} ina he tāpiri te ±. Tāpiri -3 ki te 3.

$$x=\frac{0}{-4}$$

Whakawehe 0 ki te -4.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-3±3}{-4} ina he tango te ±. Tango 3 mai i -3.

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

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

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

Kua oti te whārite te whakatau.

$$x=0 x=\frac{3}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-1.

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

Tangohia te 2x^{2} mai i ngā taha e rua.

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

Me tāpiri te 2x ki ngā taha e rua.

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

Pahekotia te x me 2x, ka 3x.

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

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.

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

Whakawehea ngā taha e rua ki te -2.

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

Mā te whakawehe ki te -2 ka wetekia te whakareanga ki te -2.

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

Whakawehe 3 ki te -2.

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

Whakawehe 0 ki te -2.

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

Whakawehea te -\frac{3}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{4}. Nā, tāpiria te pūrua o te -\frac{3}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia -\frac{3}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{3}{2}x+\frac{9}{16}=\frac{9}{16}$$

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

$$\left(x-\frac{3}{4}\right)^{2}=\frac{9}{16}$$

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

$$\sqrt{\left(x-\frac{3}{4}\right)^{2}}=\sqrt{\frac{9}{16}}$$

Whakarūnātia.

$$x-\frac{3}{4}=\frac{3}{4} x-\frac{3}{4}=-\frac{3}{4}$$

Me tāpiri \frac{3}{4} ki ngā taha e rua o te whārite.

$$x=\frac{3}{2} x=0$$