Whakaoti i te 2x^2+10=0

$$2 { x }^{ 2 } +10=0$$

Whakaoti mō x (complex solution)

$$x=-\sqrt{5}i\approx -0-2.236067977i$$

$$x=\sqrt{5}i\approx 2.236067977i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 10 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$2x^{2}=-10$$

Whakawehea ngā taha e rua ki te 2.

$$x^{2}=\frac{-10}{2}$$

Whakawehea te -10 ki te 2, kia riro ko -5.

$$x^{2}=-5$$

Kua oti te whārite te whakatau.

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

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.

$$2x^{2}+10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me 10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 10}}{2\times 2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 2\times 10}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\times 10}}{2\times 2}$$

Whakareatia -8 ki te 10.

$$x=\frac{0±\sqrt{-80}}{2\times 2}$$

Tuhia te pūtakerua o te -80.

$$x=\frac{0±4\sqrt{5}i}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±4\sqrt{5}i}{4}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{5}i}{4} ina he tāpiri te ±.

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

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{5}i}{4} ina he tango te ±.

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

Kua oti te whārite te whakatau.

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