Whakaoti i te 4x^2+2x/3=0

$$4 { x }^{ 2 } + \frac{ 2x }{ 3 } =0$$

Whakaoti mō x

$$x=-\frac{1}{6}\approx -0.166666667$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakareatia ngā taha e rua o te whārite ki te 3.

$$12x^{2}+2x=0$$

Tauwehea te x.

$$x\left(12x+2\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 12x+2=0.

$$x=0 x=-\frac{1}{6}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 3.

$$12x^{2}+2x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 12 mō a, 2 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Tuhia te pūtakerua o te 2^{2}.

$$x=\frac{-2±2}{2\times 12}$$

Whakareatia 2 ki te 12.

$$x=\frac{-2±2}{24}$$

Nā, me whakaoti te whārite x=\frac{-2±2}{24} ina he tāpiri te ±. Tāpiri -2 ki te 2.

$$x=\frac{0}{24}$$

Whakawehe 0 ki te 24.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-2±2}{24} ina he tango te ±. Tango 2 mai i -2.

$$x=-\frac{4}{24}$$

Whakahekea te hautanga \frac{-4}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Kua oti te whārite te whakatau.

$$x=0 x=-\frac{1}{6}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 3.

$$12x^{2}+2x=0$$

Whakawehea ngā taha e rua ki te 12.

$$\frac{12x^{2}+2x}{12}=\frac{0}{12}$$

Mā te whakawehe ki te 12 ka wetekia te whakareanga ki te 12.

$$x^{2}+\frac{2}{12}x=\frac{0}{12}$$

Whakahekea te hautanga \frac{2}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}+\frac{1}{6}x=\frac{0}{12}$$

Whakawehe 0 ki te 12.

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

Whakawehea te \frac{1}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{12}. Nā, tāpiria te pūrua o te \frac{1}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{1}{6}x+\left(\frac{1}{12}\right)^{2}=\left(\frac{1}{12}\right)^{2}$$

Pūruatia \frac{1}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{1}{6}x+\frac{1}{144}=\frac{1}{144}$$

Tauwehea x^{2}+\frac{1}{6}x+\frac{1}{144}. 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}.

$$\left(x+\frac{1}{12}\right)^{2}=\frac{1}{144}$$

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

$$\sqrt{\left(x+\frac{1}{12}\right)^{2}}=\sqrt{\frac{1}{144}}$$

Whakarūnātia.

$$x+\frac{1}{12}=\frac{1}{12} x+\frac{1}{12}=-\frac{1}{12}$$

Me tango \frac{1}{12} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{1}{6}$$