Whakaoti i te -1/3x+2=-x^2+7/2x+2

$$- \frac { 1 } { 3 } x + 2 = - x ^ { 2 } + \frac { 7 } { 2 } x + 2$$

Whakaoti mō x

$$x = \frac{23}{6} = 3\frac{5}{6} \approx 3.833333333$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Me tāpiri te x^{2} ki ngā taha e rua.

$$-\frac{1}{3}x+2+x^{2}=\frac{7}{2}x+2$$

Tangohia te \frac{7}{2}x mai i ngā taha e rua.

$$-\frac{1}{3}x+2+x^{2}-\frac{7}{2}x=2$$

Pahekotia te -\frac{1}{3}x me -\frac{7}{2}x, ka -\frac{23}{6}x.

$$-\frac{23}{6}x+2+x^{2}=2$$

Tangohia te 2 mai i ngā taha e rua.

$$-\frac{23}{6}x+2+x^{2}-2=0$$

Tangohia te 2 i te 2, ka 0.

$$-\frac{23}{6}x+x^{2}=0$$

Tauwehea te x.

$$x\left(-\frac{23}{6}+x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -\frac{23}{6}+x=0.

$$x=0 x=\frac{23}{6}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te x^{2} ki ngā taha e rua.

$$-\frac{1}{3}x+2+x^{2}=\frac{7}{2}x+2$$

Tangohia te \frac{7}{2}x mai i ngā taha e rua.

$$-\frac{1}{3}x+2+x^{2}-\frac{7}{2}x=2$$

Pahekotia te -\frac{1}{3}x me -\frac{7}{2}x, ka -\frac{23}{6}x.

$$-\frac{23}{6}x+2+x^{2}=2$$

Tangohia te 2 mai i ngā taha e rua.

$$-\frac{23}{6}x+2+x^{2}-2=0$$

Tangohia te 2 i te 2, ka 0.

$$-\frac{23}{6}x+x^{2}=0$$

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.

$$x^{2}-\frac{23}{6}x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -\frac{23}{6} mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{23}{6}\right)±\sqrt{\left(-\frac{23}{6}\right)^{2}}}{2}$$

Tuhia te pūtakerua o te \left(-\frac{23}{6}\right)^{2}.

$$x=\frac{-\left(-\frac{23}{6}\right)±\frac{23}{6}}{2}$$

Ko te tauaro o -\frac{23}{6} ko \frac{23}{6}.

$$x=\frac{\frac{23}{6}±\frac{23}{6}}{2}$$

Nā, me whakaoti te whārite x=\frac{\frac{23}{6}±\frac{23}{6}}{2} ina he tāpiri te ±. Tāpiri \frac{23}{6} ki te \frac{23}{6} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{\frac{23}{3}}{2}$$

Whakawehe \frac{23}{3} ki te 2.

$$x=\frac{23}{6}$$

Nā, me whakaoti te whārite x=\frac{\frac{23}{6}±\frac{23}{6}}{2} ina he tango te ±. Tango \frac{23}{6} mai i \frac{23}{6} mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

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

Whakawehe 0 ki te 2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{23}{6} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te x^{2} ki ngā taha e rua.

$$-\frac{1}{3}x+2+x^{2}=\frac{7}{2}x+2$$

Tangohia te \frac{7}{2}x mai i ngā taha e rua.

$$-\frac{1}{3}x+2+x^{2}-\frac{7}{2}x=2$$

Pahekotia te -\frac{1}{3}x me -\frac{7}{2}x, ka -\frac{23}{6}x.

$$-\frac{23}{6}x+2+x^{2}=2$$

Tangohia te 2 mai i ngā taha e rua.

$$-\frac{23}{6}x+2+x^{2}-2=0$$

Tangohia te 2 i te 2, ka 0.

$$-\frac{23}{6}x+x^{2}=0$$

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.

$$x^{2}-\frac{23}{6}x=0$$

Whakawehea te -\frac{23}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{23}{12}. Nā, tāpiria te pūrua o te -\frac{23}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{23}{6}x+\left(-\frac{23}{12}\right)^{2}=\left(-\frac{23}{12}\right)^{2}$$

Pūruatia -\frac{23}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{23}{6}x+\frac{529}{144}=\frac{529}{144}$$

Tauwehea x^{2}-\frac{23}{6}x+\frac{529}{144}. 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}.

$$\left(x-\frac{23}{12}\right)^{2}=\frac{529}{144}$$

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

$$\sqrt{\left(x-\frac{23}{12}\right)^{2}}=\sqrt{\frac{529}{144}}$$

Whakarūnātia.

$$x-\frac{23}{12}=\frac{23}{12} x-\frac{23}{12}=-\frac{23}{12}$$

Me tāpiri \frac{23}{12} ki ngā taha e rua o te whārite.

$$x=\frac{23}{6} x=0$$