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

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

Whakaoti mō x

$$x=-\frac{1}{3}\approx -0.333333333$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

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

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

Tangohia te 4 mai i ngā taha e rua.

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

Tangohia te 4 i te 4, ka 0.

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

Tauwehea te x.

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

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

$$x=0 x=-\frac{1}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

Tangohia te 4 mai i ngā taha e rua.

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

Tangohia te 4 i te 4, ka 0.

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

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

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

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

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

Ko te tauaro o -\frac{2}{3} ko \frac{2}{3}.

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

Whakareatia 2 ki te -2.

$$x=\frac{\frac{2}{3}±\frac{2}{3}}{-4}$$

Nā, me whakaoti te whārite x=\frac{\frac{2}{3}±\frac{2}{3}}{-4} ina he tāpiri te ±. Tāpiri \frac{2}{3} ki te \frac{2}{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.

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

Whakawehe \frac{4}{3} ki te -4.

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

Nā, me whakaoti te whārite x=\frac{\frac{2}{3}±\frac{2}{3}}{-4} ina he tango te ±. Tango \frac{2}{3} mai i \frac{2}{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.

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

Whakawehe 0 ki te -4.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-\frac{1}{3} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

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

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

Tangohia te 4 mai i ngā taha e rua.

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

Tangohia te 4 i te 4, ka 0.

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

Whakawehea ngā taha e rua ki te -2.

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

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

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

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

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

Whakawehe 0 ki te -2.

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

Whakawehea te \frac{1}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{6}. Nā, tāpiria te pūrua o te \frac{1}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{1}{3}x+\left(\frac{1}{6}\right)^{2}=\left(\frac{1}{6}\right)^{2}$$

Pūruatia \frac{1}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{1}{3}x+\frac{1}{36}=\frac{1}{36}$$

Tauwehea x^{2}+\frac{1}{3}x+\frac{1}{36}. 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}.

$$\left(x+\frac{1}{6}\right)^{2}=\frac{1}{36}$$

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

$$\sqrt{\left(x+\frac{1}{6}\right)^{2}}=\sqrt{\frac{1}{36}}$$

Whakarūnātia.

$$x+\frac{1}{6}=\frac{1}{6} x+\frac{1}{6}=-\frac{1}{6}$$

Me tango \frac{1}{6} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{1}{3}$$