Whakaoti i te -4/3x=1/2x^2

$$- \frac{ 4 }{ 3 } x= \frac{ 1 }{ 2 } { x }^{ 2 }$$

Whakaoti mō x

$$x = -\frac{8}{3} = -2\frac{2}{3} \approx -2.666666667$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te \frac{1}{2}x^{2} mai i ngā taha e rua.

$$-\frac{4}{3}x-\frac{1}{2}x^{2}=0$$

Tauwehea te x.

$$x\left(-\frac{4}{3}-\frac{1}{2}x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -\frac{4}{3}-\frac{x}{2}=0.

$$x=0 x=-\frac{8}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te \frac{1}{2}x^{2} mai i ngā taha e rua.

$$-\frac{4}{3}x-\frac{1}{2}x^{2}=0$$

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.

$$-\frac{1}{2}x^{2}-\frac{4}{3}x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -\frac{1}{2} mō a, -\frac{4}{3} mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{4}{3}\right)±\sqrt{\left(-\frac{4}{3}\right)^{2}}}{2\left(-\frac{1}{2}\right)}$$

Tuhia te pūtakerua o te \left(-\frac{4}{3}\right)^{2}.

$$x=\frac{-\left(-\frac{4}{3}\right)±\frac{4}{3}}{2\left(-\frac{1}{2}\right)}$$

Ko te tauaro o -\frac{4}{3} ko \frac{4}{3}.

$$x=\frac{\frac{4}{3}±\frac{4}{3}}{2\left(-\frac{1}{2}\right)}$$

Whakareatia 2 ki te -\frac{1}{2}.

$$x=\frac{\frac{4}{3}±\frac{4}{3}}{-1}$$

Nā, me whakaoti te whārite x=\frac{\frac{4}{3}±\frac{4}{3}}{-1} ina he tāpiri te ±. Tāpiri \frac{4}{3} ki te \frac{4}{3} 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.

$$x=\frac{\frac{8}{3}}{-1}$$

Whakawehe \frac{8}{3} ki te -1.

$$x=-\frac{8}{3}$$

Nā, me whakaoti te whārite x=\frac{\frac{4}{3}±\frac{4}{3}}{-1} ina he tango te ±. Tango \frac{4}{3} mai i \frac{4}{3} 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.

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

Whakawehe 0 ki te -1.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-\frac{8}{3} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te \frac{1}{2}x^{2} mai i ngā taha e rua.

$$-\frac{4}{3}x-\frac{1}{2}x^{2}=0$$

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.

$$-\frac{1}{2}x^{2}-\frac{4}{3}x=0$$

Me whakarea ngā taha e rua ki te -2.

$$\frac{-\frac{1}{2}x^{2}-\frac{4}{3}x}{-\frac{1}{2}}=\frac{0}{-\frac{1}{2}}$$

Mā te whakawehe ki te -\frac{1}{2} ka wetekia te whakareanga ki te -\frac{1}{2}.

$$x^{2}+\left(-\frac{\frac{4}{3}}{-\frac{1}{2}}\right)x=\frac{0}{-\frac{1}{2}}$$

Whakawehe -\frac{4}{3} ki te -\frac{1}{2} mā te whakarea -\frac{4}{3} ki te tau huripoki o -\frac{1}{2}.

$$x^{2}+\frac{8}{3}x=\frac{0}{-\frac{1}{2}}$$

Whakawehe 0 ki te -\frac{1}{2} mā te whakarea 0 ki te tau huripoki o -\frac{1}{2}.

$$x^{2}+\frac{8}{3}x=0$$

Whakawehea te \frac{8}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{4}{3}. Nā, tāpiria te pūrua o te \frac{4}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{8}{3}x+\left(\frac{4}{3}\right)^{2}=\left(\frac{4}{3}\right)^{2}$$

Pūruatia \frac{4}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{8}{3}x+\frac{16}{9}=\frac{16}{9}$$

Tauwehea x^{2}+\frac{8}{3}x+\frac{16}{9}. 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}.

$$\left(x+\frac{4}{3}\right)^{2}=\frac{16}{9}$$

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

$$\sqrt{\left(x+\frac{4}{3}\right)^{2}}=\sqrt{\frac{16}{9}}$$

Whakarūnātia.

$$x+\frac{4}{3}=\frac{4}{3} x+\frac{4}{3}=-\frac{4}{3}$$

Me tango \frac{4}{3} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{8}{3}$$