Whakaoti i te 6x^2-46=0

$$6 x ^ { 2 } - 46 = 0$$

Whakaoti mō x

$$x = \frac{\sqrt{69}}{3} \approx 2.768874621$$

$$x = -\frac{\sqrt{69}}{3} \approx -2.768874621$$

Ngā Upane mā te Kimi Pūtakerua

Me tāpiri te 46 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$6x^{2}=46$$

Whakawehea ngā taha e rua ki te 6.

$$x^{2}=\frac{46}{6}$$

Whakahekea te hautanga \frac{46}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}=\frac{23}{3}$$

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

$$x=\frac{\sqrt{69}}{3} x=-\frac{\sqrt{69}}{3}$$

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.

$$6x^{2}-46=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 0 mō b, me -46 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-46\right)}}{2\times 6}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-46\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{0±\sqrt{-24\left(-46\right)}}{2\times 6}$$

Whakareatia -24 ki te -46.

$$x=\frac{0±\sqrt{1104}}{2\times 6}$$

Tuhia te pūtakerua o te 1104.

$$x=\frac{0±4\sqrt{69}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{0±4\sqrt{69}}{12}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{69}}{12} ina he tāpiri te ±.

$$x=\frac{\sqrt{69}}{3}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{69}}{12} ina he tango te ±.

$$x=-\frac{\sqrt{69}}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{69}}{3} x=-\frac{\sqrt{69}}{3}$$