Whakaoti i te m^2-6/5=m

$$\frac { m ^ { 2 } - 6 } { 5 } = m$$

Whakaoti mō m

$$m=-1$$

$$m=6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ia wā o m^{2}-6 ki te 5, kia riro ko \frac{1}{5}m^{2}-\frac{6}{5}.

$$\frac{1}{5}m^{2}-\frac{6}{5}=m$$

Tangohia te m mai i ngā taha e rua.

$$\frac{1}{5}m^{2}-\frac{6}{5}-m=0$$

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.

$$\frac{1}{5}m^{2}-m-\frac{6}{5}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{1}{5} mō a, -1 mō b, me -\frac{6}{5} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-1\right)±\sqrt{1-4\times \frac{1}{5}\left(-\frac{6}{5}\right)}}{2\times \frac{1}{5}}$$

Whakareatia -4 ki te \frac{1}{5}.

$$m=\frac{-\left(-1\right)±\sqrt{1-\frac{4}{5}\left(-\frac{6}{5}\right)}}{2\times \frac{1}{5}}$$

Whakareatia -\frac{4}{5} ki te -\frac{6}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$m=\frac{-\left(-1\right)±\sqrt{1+\frac{24}{25}}}{2\times \frac{1}{5}}$$

Tāpiri 1 ki te \frac{24}{25}.

$$m=\frac{-\left(-1\right)±\sqrt{\frac{49}{25}}}{2\times \frac{1}{5}}$$

Tuhia te pūtakerua o te \frac{49}{25}.

$$m=\frac{-\left(-1\right)±\frac{7}{5}}{2\times \frac{1}{5}}$$

Ko te tauaro o -1 ko 1.

$$m=\frac{1±\frac{7}{5}}{2\times \frac{1}{5}}$$

Whakareatia 2 ki te \frac{1}{5}.

$$m=\frac{1±\frac{7}{5}}{\frac{2}{5}}$$

Nā, me whakaoti te whārite m=\frac{1±\frac{7}{5}}{\frac{2}{5}} ina he tāpiri te ±. Tāpiri 1 ki te \frac{7}{5}.

$$m=\frac{\frac{12}{5}}{\frac{2}{5}}$$

Whakawehe \frac{12}{5} ki te \frac{2}{5} mā te whakarea \frac{12}{5} ki te tau huripoki o \frac{2}{5}.

$$m=6$$

Nā, me whakaoti te whārite m=\frac{1±\frac{7}{5}}{\frac{2}{5}} ina he tango te ±. Tango \frac{7}{5} mai i 1.

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

Whakawehe -\frac{2}{5} ki te \frac{2}{5} mā te whakarea -\frac{2}{5} ki te tau huripoki o \frac{2}{5}.

$$m=-1$$

Kua oti te whārite te whakatau.

$$m=6 m=-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawehea ia wā o m^{2}-6 ki te 5, kia riro ko \frac{1}{5}m^{2}-\frac{6}{5}.

$$\frac{1}{5}m^{2}-\frac{6}{5}=m$$

Tangohia te m mai i ngā taha e rua.

$$\frac{1}{5}m^{2}-\frac{6}{5}-m=0$$

Me tāpiri te \frac{6}{5} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$\frac{1}{5}m^{2}-m=\frac{6}{5}$$

Me whakarea ngā taha e rua ki te 5.

$$\frac{\frac{1}{5}m^{2}-m}{\frac{1}{5}}=\frac{\frac{6}{5}}{\frac{1}{5}}$$

Mā te whakawehe ki te \frac{1}{5} ka wetekia te whakareanga ki te \frac{1}{5}.

$$m^{2}+\left(-\frac{1}{\frac{1}{5}}\right)m=\frac{\frac{6}{5}}{\frac{1}{5}}$$

Whakawehe -1 ki te \frac{1}{5} mā te whakarea -1 ki te tau huripoki o \frac{1}{5}.

$$m^{2}-5m=\frac{\frac{6}{5}}{\frac{1}{5}}$$

Whakawehe \frac{6}{5} ki te \frac{1}{5} mā te whakarea \frac{6}{5} ki te tau huripoki o \frac{1}{5}.

$$m^{2}-5m=6$$

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

$$m^{2}-5m+\left(-\frac{5}{2}\right)^{2}=6+\left(-\frac{5}{2}\right)^{2}$$

Pūruatia -\frac{5}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$m^{2}-5m+\frac{25}{4}=6+\frac{25}{4}$$

Tāpiri 6 ki te \frac{25}{4}.

$$m^{2}-5m+\frac{25}{4}=\frac{49}{4}$$

Tauwehea m^{2}-5m+\frac{25}{4}. 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}.

$$\left(m-\frac{5}{2}\right)^{2}=\frac{49}{4}$$

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

$$\sqrt{\left(m-\frac{5}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Whakarūnātia.

$$m-\frac{5}{2}=\frac{7}{2} m-\frac{5}{2}=-\frac{7}{2}$$

Me tāpiri \frac{5}{2} ki ngā taha e rua o te whārite.

$$m=6 m=-1$$