Whakaoti i te 2x^2+6=x

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

Whakaoti mō x (complex solution)

$$x=\frac{1+\sqrt{47}i}{4}\approx 0.25+1.71391365i$$

$$x=\frac{-\sqrt{47}i+1}{4}\approx 0.25-1.71391365i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te x mai i ngā taha e rua.

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

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -1 mō b, me 6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 2\times 6}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-1\right)±\sqrt{1-8\times 6}}{2\times 2}$$

Whakareatia -8 ki te 6.

$$x=\frac{-\left(-1\right)±\sqrt{1-48}}{2\times 2}$$

Tāpiri 1 ki te -48.

$$x=\frac{-\left(-1\right)±\sqrt{-47}}{2\times 2}$$

Tuhia te pūtakerua o te -47.

$$x=\frac{-\left(-1\right)±\sqrt{47}i}{2\times 2}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±\sqrt{47}i}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{1±\sqrt{47}i}{4}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{47}i}{4} ina he tāpiri te ±. Tāpiri 1 ki te i\sqrt{47}.

$$x=\frac{1+\sqrt{47}i}{4}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{47}i}{4} ina he tango te ±. Tango i\sqrt{47} mai i 1.

$$x=\frac{-\sqrt{47}i+1}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{1+\sqrt{47}i}{4} x=\frac{-\sqrt{47}i+1}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te x mai i ngā taha e rua.

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

Tangohia te 6 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Whakawehea ngā taha e rua ki te 2.

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

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}-\frac{1}{2}x=-\frac{6}{2}$$

Whakawehe -6 ki te 2.

$$x^{2}-\frac{1}{2}x=-3$$

Whakawehea te -\frac{1}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{4}. Nā, tāpiria te pūrua o te -\frac{1}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{2}x+\left(-\frac{1}{4}\right)^{2}=-3+\left(-\frac{1}{4}\right)^{2}$$

Pūruatia -\frac{1}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=-3+\frac{1}{16}$$

Tāpiri -3 ki te \frac{1}{16}.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=-\frac{47}{16}$$

Tauwehea x^{2}-\frac{1}{2}x+\frac{1}{16}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{4}\right)^{2}=-\frac{47}{16}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{-\frac{47}{16}}$$

Whakarūnātia.

$$x-\frac{1}{4}=\frac{\sqrt{47}i}{4} x-\frac{1}{4}=-\frac{\sqrt{47}i}{4}$$

Me tāpiri \frac{1}{4} ki ngā taha e rua o te whārite.

$$x=\frac{1+\sqrt{47}i}{4} x=\frac{-\sqrt{47}i+1}{4}$$