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

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

Whakaoti mō x

$$x=3$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

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

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

Pahekotia te -x^{2} me -x^{2}, ka -2x^{2}.

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

Me tāpiri te 4x ki ngā taha e rua.

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

Pahekotia te 2x me 4x, ka 6x.

$$3+6x-2x^{2}=3$$

Tangohia te 3 mai i ngā taha e rua.

$$3+6x-2x^{2}-3=0$$

Tangohia te 3 i te 3, ka 0.

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

Tauwehea te x.

$$x\left(6-2x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 6-2x=0.

$$x=0 x=3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

Pahekotia te -x^{2} me -x^{2}, ka -2x^{2}.

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

Me tāpiri te 4x ki ngā taha e rua.

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

Pahekotia te 2x me 4x, ka 6x.

$$3+6x-2x^{2}=3$$

Tangohia te 3 mai i ngā taha e rua.

$$3+6x-2x^{2}-3=0$$

Tangohia te 3 i te 3, ka 0.

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

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.

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

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

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

Tuhia te pūtakerua o te 6^{2}.

$$x=\frac{-6±6}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-6±6}{-4}$$

Nā, me whakaoti te whārite x=\frac{-6±6}{-4} ina he tāpiri te ±. Tāpiri -6 ki te 6.

$$x=\frac{0}{-4}$$

Whakawehe 0 ki te -4.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-6±6}{-4} ina he tango te ±. Tango 6 mai i -6.

$$x=-\frac{12}{-4}$$

Whakawehe -12 ki te -4.

$$x=3$$

Kua oti te whārite te whakatau.

$$x=0 x=3$$

Ngā Upane mō te Whakaoti i te Pūrua

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

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

Pahekotia te -x^{2} me -x^{2}, ka -2x^{2}.

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

Me tāpiri te 4x ki ngā taha e rua.

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

Pahekotia te 2x me 4x, ka 6x.

$$3+6x-2x^{2}=3$$

Tangohia te 3 mai i ngā taha e rua.

$$6x-2x^{2}=3-3$$

Tangohia te 3 i te 3, ka 0.

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

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.

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

Whakawehea ngā taha e rua ki te -2.

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

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

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

Whakawehe 6 ki te -2.

$$x^{2}-3x=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

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

Whakawehea te -3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{2}. Nā, tāpiria te pūrua o te -\frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3x+\frac{9}{4}=\frac{9}{4}$$

Tauwehea x^{2}-3x+\frac{9}{4}. 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}.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

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

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$x=3 x=0$$