Whakaoti i te 3x^2+40=12

$$3 x ^ { 2 } + 40 = 12$$

Whakaoti mō x (complex solution)

$$x=-\frac{2\sqrt{21}i}{3}\approx -0-3.055050463i$$

$$x=\frac{2\sqrt{21}i}{3}\approx 3.055050463i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 40 mai i ngā taha e rua.

$$3x^{2}=12-40$$

Tangohia te 40 i te 12, ka -28.

$$3x^{2}=-28$$

Whakawehea ngā taha e rua ki te 3.

$$x^{2}=-\frac{28}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{21}i}{3} x=-\frac{2\sqrt{21}i}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 12 mai i ngā taha e rua.

$$3x^{2}+40-12=0$$

Tangohia te 12 i te 40, ka 28.

$$3x^{2}+28=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me 28 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 28}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\times 28}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\times 28}}{2\times 3}$$

Whakareatia -12 ki te 28.

$$x=\frac{0±\sqrt{-336}}{2\times 3}$$

Tuhia te pūtakerua o te -336.

$$x=\frac{0±4\sqrt{21}i}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±4\sqrt{21}i}{6}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{21}i}{6} ina he tāpiri te ±.

$$x=\frac{2\sqrt{21}i}{3}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{21}i}{6} ina he tango te ±.

$$x=-\frac{2\sqrt{21}i}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{21}i}{3} x=-\frac{2\sqrt{21}i}{3}$$