Whakaoti i te 003=100x-41666662x^2

$$003 = 100 x - 41666662 x ^ { 2 }$$

Whakaoti mō x

$$x=\frac{50}{20833331}\approx 0.0000024$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakareatia te 0 ki te 0, ka 0.

$$0\times 3=100x-41666662x^{2}$$

Whakareatia te 0 ki te 3, ka 0.

$$0=100x-41666662x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$100x-41666662x^{2}=0$$

Tauwehea te x.

$$x\left(100-41666662x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 100-41666662x=0.

$$x=0 x=\frac{50}{20833331}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 0, ka 0.

$$0\times 3=100x-41666662x^{2}$$

Whakareatia te 0 ki te 3, ka 0.

$$0=100x-41666662x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$100x-41666662x^{2}=0$$

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.

$$-41666662x^{2}+100x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -41666662 mō a, 100 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-100±\sqrt{100^{2}}}{2\left(-41666662\right)}$$

Tuhia te pūtakerua o te 100^{2}.

$$x=\frac{-100±100}{2\left(-41666662\right)}$$

Whakareatia 2 ki te -41666662.

$$x=\frac{-100±100}{-83333324}$$

Nā, me whakaoti te whārite x=\frac{-100±100}{-83333324} ina he tāpiri te ±. Tāpiri -100 ki te 100.

$$x=\frac{0}{-83333324}$$

Whakawehe 0 ki te -83333324.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-100±100}{-83333324} ina he tango te ±. Tango 100 mai i -100.

$$x=-\frac{200}{-83333324}$$

Whakahekea te hautanga \frac{-200}{-83333324} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{50}{20833331}$$

Kua oti te whārite te whakatau.

$$x=0 x=\frac{50}{20833331}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 0 ki te 0, ka 0.

$$0\times 3=100x-41666662x^{2}$$

Whakareatia te 0 ki te 3, ka 0.

$$0=100x-41666662x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$100x-41666662x^{2}=0$$

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.

$$-41666662x^{2}+100x=0$$

Whakawehea ngā taha e rua ki te -41666662.

$$\frac{-41666662x^{2}+100x}{-41666662}=\frac{0}{-41666662}$$

Mā te whakawehe ki te -41666662 ka wetekia te whakareanga ki te -41666662.

$$x^{2}+\frac{100}{-41666662}x=\frac{0}{-41666662}$$

Whakahekea te hautanga \frac{100}{-41666662} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{50}{20833331}x=\frac{0}{-41666662}$$

Whakawehe 0 ki te -41666662.

$$x^{2}-\frac{50}{20833331}x=0$$

Whakawehea te -\frac{50}{20833331}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{25}{20833331}. Nā, tāpiria te pūrua o te -\frac{25}{20833331} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{50}{20833331}x+\left(-\frac{25}{20833331}\right)^{2}=\left(-\frac{25}{20833331}\right)^{2}$$

Pūruatia -\frac{25}{20833331} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{50}{20833331}x+\frac{625}{434027680555561}=\frac{625}{434027680555561}$$

Tauwehea x^{2}-\frac{50}{20833331}x+\frac{625}{434027680555561}. 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}.

$$\left(x-\frac{25}{20833331}\right)^{2}=\frac{625}{434027680555561}$$

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

$$\sqrt{\left(x-\frac{25}{20833331}\right)^{2}}=\sqrt{\frac{625}{434027680555561}}$$

Whakarūnātia.

$$x-\frac{25}{20833331}=\frac{25}{20833331} x-\frac{25}{20833331}=-\frac{25}{20833331}$$

Me tāpiri \frac{25}{20833331} ki ngā taha e rua o te whārite.

$$x=\frac{50}{20833331} x=0$$