Whakaoti i te 2x(3x-1)=0

$$2x(3x-1)=0$$

Whakaoti mō x

$$x=\frac{1}{3}\approx 0.333333333$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te 3x-1.

$$6x^{2}-2x=0$$

Tauwehea te x.

$$x\left(6x-2\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 6x-2=0.

$$x=0 x=\frac{1}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te 3x-1.

$$6x^{2}-2x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, -2 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}}}{2\times 6}$$

Tuhia te pūtakerua o te \left(-2\right)^{2}.

$$x=\frac{-\left(-2\right)±2}{2\times 6}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±2}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{2±2}{12}$$

Nā, me whakaoti te whārite x=\frac{2±2}{12} ina he tāpiri te ±. Tāpiri 2 ki te 2.

$$x=\frac{4}{12}$$

Whakahekea te hautanga \frac{4}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Nā, me whakaoti te whārite x=\frac{2±2}{12} ina he tango te ±. Tango 2 mai i 2.

$$x=\frac{0}{12}$$

Whakawehe 0 ki te 12.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{3} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te 3x-1.

$$6x^{2}-2x=0$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}-2x}{6}=\frac{0}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$x^{2}+\left(-\frac{2}{6}\right)x=\frac{0}{6}$$

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

$$x^{2}-\frac{1}{3}x=\frac{0}{6}$$

Whakawehe 0 ki te 6.

$$x^{2}-\frac{1}{3}x=0$$

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.

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

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

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

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}.

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

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

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

Whakarūnātia.

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

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

$$x=\frac{1}{3} x=0$$