Whakaoti i te 2x^2+8=7

$$2 x ^ { 2 } + 8 = 7$$

Whakaoti mō x (complex solution)

$$x=-\frac{\sqrt{2}i}{2}\approx -0-0.707106781i$$

$$x=\frac{\sqrt{2}i}{2}\approx 0.707106781i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 8 mai i ngā taha e rua.

$$2x^{2}=7-8$$

Tangohia te 8 i te 7, ka -1.

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

Whakawehea ngā taha e rua ki te 2.

$$x^{2}=-\frac{1}{2}$$

Kua oti te whārite te whakatau.

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 7 mai i ngā taha e rua.

$$2x^{2}+8-7=0$$

Tangohia te 7 i te 8, ka 1.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua 0.

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

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8}}{2\times 2}$$

Tuhia te pūtakerua o te -8.

$$x=\frac{0±2\sqrt{2}i}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±2\sqrt{2}i}{4}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{2}i}{4} ina he tāpiri te ±.

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

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{2}i}{4} ina he tango te ±.

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

Kua oti te whārite te whakatau.

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