Whakaoti i te 2x^2+7=1

$$2 x ^ { 2 } + 7 = 1$$

Whakaoti mō x (complex solution)

$$x=-\sqrt{3}i\approx -0-1.732050808i$$

$$x=\sqrt{3}i\approx 1.732050808i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 7 mai i ngā taha e rua.

$$2x^{2}=1-7$$

Tangohia te 7 i te 1, ka -6.

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

Whakawehea ngā taha e rua ki te 2.

$$x^{2}=\frac{-6}{2}$$

Whakawehea te -6 ki te 2, kia riro ko -3.

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

Kua oti te whārite te whakatau.

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 1 mai i ngā taha e rua.

$$2x^{2}+7-1=0$$

Tangohia te 1 i te 7, ka 6.

$$2x^{2}+6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me 6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 6}}{2\times 2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 2\times 6}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\times 6}}{2\times 2}$$

Whakareatia -8 ki te 6.

$$x=\frac{0±\sqrt{-48}}{2\times 2}$$

Tuhia te pūtakerua o te -48.

$$x=\frac{0±4\sqrt{3}i}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±4\sqrt{3}i}{4}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{3}i}{4} ina he tāpiri te ±.

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

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{3}i}{4} ina he tango te ±.

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

Kua oti te whārite te whakatau.

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