Whakaoti i te x^2-2x=-8

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

Whakaoti mō x (complex solution)

$$x=1+\sqrt{7}i\approx 1+2.645751311i$$

$$x=-\sqrt{7}i+1\approx 1-2.645751311i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

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

Me tāpiri 8 ki ngā taha e rua o te whārite.

$$x^{2}-2x-\left(-8\right)=-8-\left(-8\right)$$

Mā te tango i te -8 i a ia ake anō ka toe ko te 0.

$$x^{2}-2x-\left(-8\right)=0$$

Tango -8 mai i 0.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me 8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 8}}{2}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times 8}}{2}$$

Whakareatia -4 ki te 8.

$$x=\frac{-\left(-2\right)±\sqrt{4-32}}{2}$$

Tāpiri 4 ki te -32.

$$x=\frac{-\left(-2\right)±\sqrt{-28}}{2}$$

Tuhia te pūtakerua o te -28.

$$x=\frac{-\left(-2\right)±2\sqrt{7}i}{2}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±2\sqrt{7}i}{2}$$

Nā, me whakaoti te whārite x=\frac{2±2\sqrt{7}i}{2} ina he tāpiri te ±. Tāpiri 2 ki te 2i\sqrt{7}.

$$x=\frac{2+2\sqrt{7}i}{2}$$

Whakawehe 2+2i\sqrt{7} ki te 2.

$$x=1+\sqrt{7}i$$

Nā, me whakaoti te whārite x=\frac{2±2\sqrt{7}i}{2} ina he tango te ±. Tango 2i\sqrt{7} mai i 2.

$$x=\frac{-2\sqrt{7}i+2}{2}$$

Whakawehe 2-2i\sqrt{7} ki te 2.

$$x=-\sqrt{7}i+1$$

Kua oti te whārite te whakatau.

$$x=1+\sqrt{7}i x=-\sqrt{7}i+1$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

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

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

$$x^{2}-2x+1=-8+1$$

Tāpiri -8 ki te 1.

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

Tauwehea x^{2}-2x+1. 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}.

$$\left(x-1\right)^{2}=-7$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{-7}$$

Whakarūnātia.

$$x-1=\sqrt{7}i x-1=-\sqrt{7}i$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=1+\sqrt{7}i x=-\sqrt{7}i+1$$