Whakaoti i te 6x^2+108=0

$$6 { x }^{ 2 } +108=0$$

Whakaoti mō x (complex solution)

$$x=-3\sqrt{2}i\approx -0-4.242640687i$$

$$x=3\sqrt{2}i\approx 4.242640687i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 108 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$6x^{2}=-108$$

Whakawehea ngā taha e rua ki te 6.

$$x^{2}=\frac{-108}{6}$$

Whakawehea te -108 ki te 6, kia riro ko -18.

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

Kua oti te whārite te whakatau.

$$x=3\sqrt{2}i x=-3\sqrt{2}i$$

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.

$$6x^{2}+108=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 0 mō b, me 108 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\times 108}}{2\times 6}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 6\times 108}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{0±\sqrt{-24\times 108}}{2\times 6}$$

Whakareatia -24 ki te 108.

$$x=\frac{0±\sqrt{-2592}}{2\times 6}$$

Tuhia te pūtakerua o te -2592.

$$x=\frac{0±36\sqrt{2}i}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{0±36\sqrt{2}i}{12}$$

Nā, me whakaoti te whārite x=\frac{0±36\sqrt{2}i}{12} ina he tāpiri te ±.

$$x=3\sqrt{2}i$$

Nā, me whakaoti te whārite x=\frac{0±36\sqrt{2}i}{12} ina he tango te ±.

$$x=-3\sqrt{2}i$$

Kua oti te whārite te whakatau.

$$x=3\sqrt{2}i x=-3\sqrt{2}i$$