Whakaoti i te 5/68+29/6*x^2=2

$$\frac{ 5 }{ 6 } 8+2 \frac{ 9 }{ 6 } \times { x }^{ 2 } =2$$

Whakaoti mō x (complex solution)

$$x=-\frac{2\sqrt{3}i}{3}\approx -0-1.154700538i$$

$$x=\frac{2\sqrt{3}i}{3}\approx 1.154700538i$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia ngā taha e rua o te whārite ki te 6.

$$5\times 8+\left(2\times 6+9\right)x^{2}=12$$

Whakareatia te 5 ki te 8, ka 40.

$$40+\left(2\times 6+9\right)x^{2}=12$$

Whakareatia te 2 ki te 6, ka 12.

$$40+\left(12+9\right)x^{2}=12$$

Tāpirihia te 12 ki te 9, ka 21.

$$40+21x^{2}=12$$

Tangohia te 40 mai i ngā taha e rua.

$$21x^{2}=12-40$$

Tangohia te 40 i te 12, ka -28.

$$21x^{2}=-28$$

Whakawehea ngā taha e rua ki te 21.

$$x^{2}=\frac{-28}{21}$$

Whakahekea te hautanga \frac{-28}{21} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$x^{2}=-\frac{4}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{3}i}{3} x=-\frac{2\sqrt{3}i}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 6.

$$5\times 8+\left(2\times 6+9\right)x^{2}=12$$

Whakareatia te 5 ki te 8, ka 40.

$$40+\left(2\times 6+9\right)x^{2}=12$$

Whakareatia te 2 ki te 6, ka 12.

$$40+\left(12+9\right)x^{2}=12$$

Tāpirihia te 12 ki te 9, ka 21.

$$40+21x^{2}=12$$

Tangohia te 12 mai i ngā taha e rua.

$$40+21x^{2}-12=0$$

Tangohia te 12 i te 40, ka 28.

$$28+21x^{2}=0$$

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.

$$21x^{2}+28=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 21 mō a, 0 mō b, me 28 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 21\times 28}}{2\times 21}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 21\times 28}}{2\times 21}$$

Whakareatia -4 ki te 21.

$$x=\frac{0±\sqrt{-84\times 28}}{2\times 21}$$

Whakareatia -84 ki te 28.

$$x=\frac{0±\sqrt{-2352}}{2\times 21}$$

Tuhia te pūtakerua o te -2352.

$$x=\frac{0±28\sqrt{3}i}{2\times 21}$$

Whakareatia 2 ki te 21.

$$x=\frac{0±28\sqrt{3}i}{42}$$

Nā, me whakaoti te whārite x=\frac{0±28\sqrt{3}i}{42} ina he tāpiri te ±.

$$x=\frac{2\sqrt{3}i}{3}$$

Nā, me whakaoti te whārite x=\frac{0±28\sqrt{3}i}{42} ina he tango te ±.

$$x=-\frac{2\sqrt{3}i}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{3}i}{3} x=-\frac{2\sqrt{3}i}{3}$$