Whakaoti i te x-x^2-3x+4-4=0

$$x - x ^ { 2 } - 3 x + 4 - 4 = 0$$

Whakaoti mō x

$$x=-2$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Pahekotia te x me -3x, ka -2x.

$$-2x-x^{2}+4-4=0$$

Tangohia te 4 i te 4, ka 0.

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

Tauwehea te x.

$$x\left(-2-x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -2-x=0.

$$x=0 x=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te x me -3x, ka -2x.

$$-2x-x^{2}+4-4=0$$

Tangohia te 4 i te 4, ka 0.

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

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.

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

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

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

Tuhia te pūtakerua o te \left(-2\right)^{2}.

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

Ko te tauaro o -2 ko 2.

$$x=\frac{2±2}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{2±2}{-2}$$

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

$$x=\frac{4}{-2}$$

Whakawehe 4 ki te -2.

$$x=-2$$

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

$$x=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-2 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te x me -3x, ka -2x.

$$-2x-x^{2}+4-4=0$$

Tangohia te 4 i te 4, ka 0.

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

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.

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

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-2x}{-1}=\frac{0}{-1}$$

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

$$x^{2}+\left(-\frac{2}{-1}\right)x=\frac{0}{-1}$$

Whakawehe -2 ki te -1.

$$x^{2}+2x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

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

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.

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

Pūrua 1.

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

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}.

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

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

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

Whakarūnātia.

$$x+1=1 x+1=-1$$

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

$$x=0 x=-2$$