Whakaoti i te 9x^2+25=0

$$9 { x }^{ 2 } +25 = 0$$

Whakaoti mō x (complex solution)

$$x=-\frac{5}{3}i\approx -1.666666667i$$

$$x=\frac{5}{3}i\approx 1.666666667i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 25 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$9x^{2}=-25$$

Whakawehea ngā taha e rua ki te 9.

$$x^{2}=-\frac{25}{9}$$

Kua oti te whārite te whakatau.

$$x=\frac{5}{3}i x=-\frac{5}{3}i$$

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.

$$9x^{2}+25=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, 0 mō b, me 25 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\times 25}}{2\times 9}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 9\times 25}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{0±\sqrt{-36\times 25}}{2\times 9}$$

Whakareatia -36 ki te 25.

$$x=\frac{0±\sqrt{-900}}{2\times 9}$$

Tuhia te pūtakerua o te -900.

$$x=\frac{0±30i}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{0±30i}{18}$$

Nā, me whakaoti te whārite x=\frac{0±30i}{18} ina he tāpiri te ±.

$$x=\frac{5}{3}i$$

Nā, me whakaoti te whārite x=\frac{0±30i}{18} ina he tango te ±.

$$x=-\frac{5}{3}i$$

Kua oti te whārite te whakatau.

$$x=\frac{5}{3}i x=-\frac{5}{3}i$$