Whakaoti i te 4m^2-36m+26=0

$$4 m ^ { 2 } - 36 m + 26 = 0$$

Whakaoti mō m

$$m = \frac{\sqrt{55} + 9}{2} \approx 8.208099244$$

$$m=\frac{9-\sqrt{55}}{2}\approx 0.791900756$$

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.

$$4m^{2}-36m+26=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, -36 mō b, me 26 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 4\times 26}}{2\times 4}$$

Pūrua -36.

$$m=\frac{-\left(-36\right)±\sqrt{1296-4\times 4\times 26}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$m=\frac{-\left(-36\right)±\sqrt{1296-16\times 26}}{2\times 4}$$

Whakareatia -16 ki te 26.

$$m=\frac{-\left(-36\right)±\sqrt{1296-416}}{2\times 4}$$

Tāpiri 1296 ki te -416.

$$m=\frac{-\left(-36\right)±\sqrt{880}}{2\times 4}$$

Tuhia te pūtakerua o te 880.

$$m=\frac{-\left(-36\right)±4\sqrt{55}}{2\times 4}$$

Ko te tauaro o -36 ko 36.

$$m=\frac{36±4\sqrt{55}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$m=\frac{36±4\sqrt{55}}{8}$$

Nā, me whakaoti te whārite m=\frac{36±4\sqrt{55}}{8} ina he tāpiri te ±. Tāpiri 36 ki te 4\sqrt{55}.

$$m=\frac{4\sqrt{55}+36}{8}$$

Whakawehe 36+4\sqrt{55} ki te 8.

$$m=\frac{\sqrt{55}+9}{2}$$

Nā, me whakaoti te whārite m=\frac{36±4\sqrt{55}}{8} ina he tango te ±. Tango 4\sqrt{55} mai i 36.

$$m=\frac{36-4\sqrt{55}}{8}$$

Whakawehe 36-4\sqrt{55} ki te 8.

$$m=\frac{9-\sqrt{55}}{2}$$

Kua oti te whārite te whakatau.

$$m=\frac{\sqrt{55}+9}{2} m=\frac{9-\sqrt{55}}{2}$$

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.

$$4m^{2}-36m+26=0$$

Me tango 26 mai i ngā taha e rua o te whārite.

$$4m^{2}-36m+26-26=-26$$

Mā te tango i te 26 i a ia ake anō ka toe ko te 0.

$$4m^{2}-36m=-26$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4m^{2}-36m}{4}=-\frac{26}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$m^{2}+\left(-\frac{36}{4}\right)m=-\frac{26}{4}$$

Whakawehe -36 ki te 4.

$$m^{2}-9m=-\frac{26}{4}$$

Whakahekea te hautanga \frac{-26}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$m^{2}-9m=-\frac{13}{2}$$

Whakawehea te -9, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{2}. Nā, tāpiria te pūrua o te -\frac{9}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$m^{2}-9m+\left(-\frac{9}{2}\right)^{2}=-\frac{13}{2}+\left(-\frac{9}{2}\right)^{2}$$

Pūruatia -\frac{9}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$m^{2}-9m+\frac{81}{4}=-\frac{13}{2}+\frac{81}{4}$$

Tāpiri -\frac{13}{2} ki te \frac{81}{4} 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.

$$m^{2}-9m+\frac{81}{4}=\frac{55}{4}$$

Tauwehea m^{2}-9m+\frac{81}{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}.

$$\left(m-\frac{9}{2}\right)^{2}=\frac{55}{4}$$

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

$$\sqrt{\left(m-\frac{9}{2}\right)^{2}}=\sqrt{\frac{55}{4}}$$

Whakarūnātia.

$$m-\frac{9}{2}=\frac{\sqrt{55}}{2} m-\frac{9}{2}=-\frac{\sqrt{55}}{2}$$

Me tāpiri \frac{9}{2} ki ngā taha e rua o te whārite.

$$m=\frac{\sqrt{55}+9}{2} m=\frac{9-\sqrt{55}}{2}$$