Whakaoti i te 5m^2-m=0

$$5 m ^ { 2 } - m = 0$$

Whakaoti mō m

$$m=\frac{1}{5}=0.2$$

$$m=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te m.

$$m\left(5m-1\right)=0$$

Hei kimi otinga whārite, me whakaoti te m=0 me te 5m-1=0.

$$m=0 m=\frac{1}{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$5m^{2}-m=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, -1 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-1\right)±\sqrt{1}}{2\times 5}$$

Tuhia te pūtakerua o te 1.

$$m=\frac{-\left(-1\right)±1}{2\times 5}$$

Ko te tauaro o -1 ko 1.

$$m=\frac{1±1}{2\times 5}$$

Whakareatia 2 ki te 5.

$$m=\frac{1±1}{10}$$

Nā, me whakaoti te whārite m=\frac{1±1}{10} ina he tāpiri te ±. Tāpiri 1 ki te 1.

$$m=\frac{2}{10}$$

Whakahekea te hautanga \frac{2}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$m=\frac{1}{5}$$

Nā, me whakaoti te whārite m=\frac{1±1}{10} ina he tango te ±. Tango 1 mai i 1.

$$m=\frac{0}{10}$$

Whakawehe 0 ki te 10.

$$m=0$$

Kua oti te whārite te whakatau.

$$m=\frac{1}{5} m=0$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$5m^{2}-m=0$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5m^{2}-m}{5}=\frac{0}{5}$$

Mā te whakawehe ki te 5 ka wetekia te whakareanga ki te 5.

$$m^{2}-\frac{1}{5}m=\frac{0}{5}$$

Whakawehe 0 ki te 5.

$$m^{2}-\frac{1}{5}m=0$$

Whakawehea te -\frac{1}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{10}. Nā, tāpiria te pūrua o te -\frac{1}{10} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$m^{2}-\frac{1}{5}m+\left(-\frac{1}{10}\right)^{2}=\left(-\frac{1}{10}\right)^{2}$$

Pūruatia -\frac{1}{10} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$m^{2}-\frac{1}{5}m+\frac{1}{100}=\frac{1}{100}$$

Tauwehea m^{2}-\frac{1}{5}m+\frac{1}{100}. 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}.

$$\left(m-\frac{1}{10}\right)^{2}=\frac{1}{100}$$

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

$$\sqrt{\left(m-\frac{1}{10}\right)^{2}}=\sqrt{\frac{1}{100}}$$

Whakarūnātia.

$$m-\frac{1}{10}=\frac{1}{10} m-\frac{1}{10}=-\frac{1}{10}$$

Me tāpiri \frac{1}{10} ki ngā taha e rua o te whārite.

$$m=\frac{1}{5} m=0$$