Whakaoti i te 2x(9x-3)=0

$$2x(9x-3)=0$$

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 9x-3.

$$18x^{2}-6x=0$$

Tauwehea te x.

$$x\left(18x-6\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 18x-6=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 9x-3.

$$18x^{2}-6x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 18 mō a, -6 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\times 18}$$

Tuhia te pūtakerua o te \left(-6\right)^{2}.

$$x=\frac{-\left(-6\right)±6}{2\times 18}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±6}{2\times 18}$$

Whakareatia 2 ki te 18.

$$x=\frac{6±6}{36}$$

Nā, me whakaoti te whārite x=\frac{6±6}{36} ina he tāpiri te ±. Tāpiri 6 ki te 6.

$$x=\frac{12}{36}$$

Whakahekea te hautanga \frac{12}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

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

Nā, me whakaoti te whārite x=\frac{6±6}{36} ina he tango te ±. Tango 6 mai i 6.

$$x=\frac{0}{36}$$

Whakawehe 0 ki te 36.

$$x=0$$

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 9x-3.

$$18x^{2}-6x=0$$

Whakawehea ngā taha e rua ki te 18.

$$\frac{18x^{2}-6x}{18}=\frac{0}{18}$$

Mā te whakawehe ki te 18 ka wetekia te whakareanga ki te 18.

$$x^{2}+\left(-\frac{6}{18}\right)x=\frac{0}{18}$$

Whakahekea te hautanga \frac{-6}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x^{2}-\frac{1}{3}x=\frac{0}{18}$$

Whakawehe 0 ki te 18.

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

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.

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