Whakaoti i te 5x^2+27=6

$$5 x ^ { 2 } + 27 = 6$$

Whakaoti mō x (complex solution)

$$x=-\frac{\sqrt{105}i}{5}\approx -0-2.049390153i$$

$$x=\frac{\sqrt{105}i}{5}\approx 2.049390153i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 27 mai i ngā taha e rua.

$$5x^{2}=6-27$$

Tangohia te 27 i te 6, ka -21.

$$5x^{2}=-21$$

Whakawehea ngā taha e rua ki te 5.

$$x^{2}=-\frac{21}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{105}i}{5} x=-\frac{\sqrt{105}i}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 6 mai i ngā taha e rua.

$$5x^{2}+27-6=0$$

Tangohia te 6 i te 27, ka 21.

$$5x^{2}+21=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, 0 mō b, me 21 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\times 21}}{2\times 5}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 5\times 21}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{0±\sqrt{-20\times 21}}{2\times 5}$$

Whakareatia -20 ki te 21.

$$x=\frac{0±\sqrt{-420}}{2\times 5}$$

Tuhia te pūtakerua o te -420.

$$x=\frac{0±2\sqrt{105}i}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{0±2\sqrt{105}i}{10}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{105}i}{10} ina he tāpiri te ±.

$$x=\frac{\sqrt{105}i}{5}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{105}i}{10} ina he tango te ±.

$$x=-\frac{\sqrt{105}i}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{105}i}{5} x=-\frac{\sqrt{105}i}{5}$$