Whakaoti i te 7x^2+5=0

$$7 x ^ { 2 } + 5 = 0$$

Whakaoti mō x (complex solution)

$$x=-\frac{\sqrt{35}i}{7}\approx -0-0.845154255i$$

$$x=\frac{\sqrt{35}i}{7}\approx 0.845154255i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 5 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$7x^{2}=-5$$

Whakawehea ngā taha e rua ki te 7.

$$x^{2}=-\frac{5}{7}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{35}i}{7} x=-\frac{\sqrt{35}i}{7}$$

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.

$$7x^{2}+5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 7 mō a, 0 mō b, me 5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\times 5}}{2\times 7}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 7\times 5}}{2\times 7}$$

Whakareatia -4 ki te 7.

$$x=\frac{0±\sqrt{-28\times 5}}{2\times 7}$$

Whakareatia -28 ki te 5.

$$x=\frac{0±\sqrt{-140}}{2\times 7}$$

Tuhia te pūtakerua o te -140.

$$x=\frac{0±2\sqrt{35}i}{2\times 7}$$

Whakareatia 2 ki te 7.

$$x=\frac{0±2\sqrt{35}i}{14}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{35}i}{14} ina he tāpiri te ±.

$$x=\frac{\sqrt{35}i}{7}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{35}i}{14} ina he tango te ±.

$$x=-\frac{\sqrt{35}i}{7}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{35}i}{7} x=-\frac{\sqrt{35}i}{7}$$