Whakaoti i te 6x^2-3/8=0

$$6 x ^ { 2 } - \frac { 3 } { 8 } = 0$$

Whakaoti mō x

$$x=\frac{1}{4}=0.25$$

$$x=-\frac{1}{4}=-0.25$$

Ngā Hipanga Whakamahi Rerekētanga o ngā Pūrua

Whakawehea ngā taha e rua ki te \frac{3}{8}.

$$16x^{2}-1=0$$

Whakaarohia te 16x^{2}-1. Tuhia anō te 16x^{2}-1 hei \left(4x\right)^{2}-1^{2}. Ka taea te rerekētanga o ngā pūrua te whakatauwehe mā te ture: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(4x-1\right)\left(4x+1\right)=0$$

Hei kimi otinga whārite, me whakaoti te 4x-1=0 me te 4x+1=0.

$$x=\frac{1}{4} x=-\frac{1}{4}$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te \frac{3}{8} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$6x^{2}=\frac{3}{8}$$

Whakawehea ngā taha e rua ki te 6.

$$x^{2}=\frac{\frac{3}{8}}{6}$$

Tuhia te \frac{\frac{3}{8}}{6} hei hautanga kotahi.

$$x^{2}=\frac{3}{8\times 6}$$

Whakareatia te 8 ki te 6, ka 48.

$$x^{2}=\frac{3}{48}$$

Whakahekea te hautanga \frac{3}{48} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x^{2}=\frac{1}{16}$$

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

$$x=\frac{1}{4} x=-\frac{1}{4}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$6x^{2}-\frac{3}{8}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 0 mō b, me -\frac{3}{8} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-\frac{3}{8}\right)}}{2\times 6}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-\frac{3}{8}\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{0±\sqrt{-24\left(-\frac{3}{8}\right)}}{2\times 6}$$

Whakareatia -24 ki te -\frac{3}{8}.

$$x=\frac{0±\sqrt{9}}{2\times 6}$$

Tuhia te pūtakerua o te 9.

$$x=\frac{0±3}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{0±3}{12}$$

Nā, me whakaoti te whārite x=\frac{0±3}{12} ina he tāpiri te ±. Whakahekea te hautanga \frac{3}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x=\frac{1}{4}$$

Nā, me whakaoti te whārite x=\frac{0±3}{12} ina he tango te ±. Whakahekea te hautanga \frac{-3}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x=-\frac{1}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{4} x=-\frac{1}{4}$$