Whakaoti i te 2x^2+100=0

$$2 x ^ { 2 } + 100 = 0$$

Whakaoti mō x (complex solution)

$$x=-5\sqrt{2}i\approx -0-7.071067812i$$

$$x=5\sqrt{2}i\approx 7.071067812i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 100 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$2x^{2}=-100$$

Whakawehea ngā taha e rua ki te 2.

$$x^{2}=\frac{-100}{2}$$

Whakawehea te -100 ki te 2, kia riro ko -50.

$$x^{2}=-50$$

Kua oti te whārite te whakatau.

$$x=5\sqrt{2}i x=-5\sqrt{2}i$$

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.

$$2x^{2}+100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me 100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 100}}{2\times 2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 2\times 100}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\times 100}}{2\times 2}$$

Whakareatia -8 ki te 100.

$$x=\frac{0±\sqrt{-800}}{2\times 2}$$

Tuhia te pūtakerua o te -800.

$$x=\frac{0±20\sqrt{2}i}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±20\sqrt{2}i}{4}$$

Nā, me whakaoti te whārite x=\frac{0±20\sqrt{2}i}{4} ina he tāpiri te ±.

$$x=5\sqrt{2}i$$

Nā, me whakaoti te whārite x=\frac{0±20\sqrt{2}i}{4} ina he tango te ±.

$$x=-5\sqrt{2}i$$

Kua oti te whārite te whakatau.

$$x=5\sqrt{2}i x=-5\sqrt{2}i$$