Whakaoti i te 6a^2-5a-1/6=0

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

Whakaoti mō a

$$a=\frac{\sqrt{29}+5}{12}\approx 0.865430401$$

$$a=\frac{5-\sqrt{29}}{12}\approx -0.032097067$$

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.

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

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

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

Pūrua -5.

$$a=\frac{-\left(-5\right)±\sqrt{25-4\times 6\left(-\frac{1}{6}\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$a=\frac{-\left(-5\right)±\sqrt{25-24\left(-\frac{1}{6}\right)}}{2\times 6}$$

Whakareatia -24 ki te -\frac{1}{6}.

$$a=\frac{-\left(-5\right)±\sqrt{25+4}}{2\times 6}$$

Tāpiri 25 ki te 4.

$$a=\frac{-\left(-5\right)±\sqrt{29}}{2\times 6}$$

Ko te tauaro o -5 ko 5.

$$a=\frac{5±\sqrt{29}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$a=\frac{5±\sqrt{29}}{12}$$

Nā, me whakaoti te whārite a=\frac{5±\sqrt{29}}{12} ina he tāpiri te ±. Tāpiri 5 ki te \sqrt{29}.

$$a=\frac{\sqrt{29}+5}{12}$$

Nā, me whakaoti te whārite a=\frac{5±\sqrt{29}}{12} ina he tango te ±. Tango \sqrt{29} mai i 5.

$$a=\frac{5-\sqrt{29}}{12}$$

Kua oti te whārite te whakatau.

$$a=\frac{\sqrt{29}+5}{12} a=\frac{5-\sqrt{29}}{12}$$

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.

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

Me tāpiri \frac{1}{6} ki ngā taha e rua o te whārite.

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

Mā te tango i te -\frac{1}{6} i a ia ake anō ka toe ko te 0.

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

Tango -\frac{1}{6} mai i 0.

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

Whakawehea ngā taha e rua ki te 6.

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

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

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

Whakawehe \frac{1}{6} ki te 6.

$$a^{2}-\frac{5}{6}a=\frac{1}{36}$$

Whakawehea te -\frac{5}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{12}. Nā, tāpiria te pūrua o te -\frac{5}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}-\frac{5}{6}a+\left(-\frac{5}{12}\right)^{2}=\frac{1}{36}+\left(-\frac{5}{12}\right)^{2}$$

Pūruatia -\frac{5}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$a^{2}-\frac{5}{6}a+\frac{25}{144}=\frac{1}{36}+\frac{25}{144}$$

Tāpiri \frac{1}{36} ki te \frac{25}{144} 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.

$$a^{2}-\frac{5}{6}a+\frac{25}{144}=\frac{29}{144}$$

Tauwehea a^{2}-\frac{5}{6}a+\frac{25}{144}. 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}.

$$\left(a-\frac{5}{12}\right)^{2}=\frac{29}{144}$$

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

$$\sqrt{\left(a-\frac{5}{12}\right)^{2}}=\sqrt{\frac{29}{144}}$$

Whakarūnātia.

$$a-\frac{5}{12}=\frac{\sqrt{29}}{12} a-\frac{5}{12}=-\frac{\sqrt{29}}{12}$$

Me tāpiri \frac{5}{12} ki ngā taha e rua o te whārite.

$$a=\frac{\sqrt{29}+5}{12} a=\frac{5-\sqrt{29}}{12}$$