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

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

Whakaoti mō x (complex solution)

$$x=-1-3i$$

$$x=-1+3i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te x^{2} mai i ngā taha e rua.

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

Tangohia te 8 mai i ngā taha e rua.

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

Tangohia te 8 i te -2, ka -10.

$$-2x-10-x^{2}=0$$

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.

$$-x^{2}-2x-10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, -2 mō b, me -10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-1\right)\left(-10\right)}}{2\left(-1\right)}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-1\right)\left(-10\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-2\right)±\sqrt{4+4\left(-10\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -10.

$$x=\frac{-\left(-2\right)±\sqrt{4-40}}{2\left(-1\right)}$$

Tāpiri 4 ki te -40.

$$x=\frac{-\left(-2\right)±\sqrt{-36}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te -36.

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

Ko te tauaro o -2 ko 2.

$$x=\frac{2±6i}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{2±6i}{-2}$$

Nā, me whakaoti te whārite x=\frac{2±6i}{-2} ina he tāpiri te ±. Tāpiri 2 ki te 6i.

$$x=\frac{2+6i}{-2}$$

Whakawehe 2+6i ki te -2.

$$x=-1-3i$$

Nā, me whakaoti te whārite x=\frac{2±6i}{-2} ina he tango te ±. Tango 6i mai i 2.

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

Whakawehe 2-6i ki te -2.

$$x=-1+3i$$

Kua oti te whārite te whakatau.

$$x=-1-3i x=-1+3i$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te x^{2} mai i ngā taha e rua.

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

Me tāpiri te 2 ki ngā taha e rua.

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

Tāpirihia te 8 ki te 2, ka 10.

$$-2x-x^{2}=10$$

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.

$$-x^{2}-2x=10$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-2x}{-1}=\frac{10}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\left(-\frac{2}{-1}\right)x=\frac{10}{-1}$$

Whakawehe -2 ki te -1.

$$x^{2}+2x=\frac{10}{-1}$$

Whakawehe 10 ki te -1.

$$x^{2}+2x=-10$$

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.

$$x^{2}+2x+1^{2}=-10+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=-10+1$$

Tāpiri -10 ki te 1.

$$x^{2}+2x+1=-9$$

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

$$\left(x+1\right)^{2}=-9$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{-9}$$

Whakarūnātia.

$$x+1=3i x+1=-3i$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=-1+3i x=-1-3i$$