Whakaoti i te 36x^2+2x-6=0

$$36 x ^ { 2 } + 2 x - 6 = 0$$

Whakaoti mō x

$$x=\frac{\sqrt{217}-1}{36}\approx 0.381414441$$

$$x=\frac{-\sqrt{217}-1}{36}\approx -0.436969996$$

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.

$$36x^{2}+2x-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 36 mō a, 2 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\times 36\left(-6\right)}}{2\times 36}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\times 36\left(-6\right)}}{2\times 36}$$

Whakareatia -4 ki te 36.

$$x=\frac{-2±\sqrt{4-144\left(-6\right)}}{2\times 36}$$

Whakareatia -144 ki te -6.

$$x=\frac{-2±\sqrt{4+864}}{2\times 36}$$

Tāpiri 4 ki te 864.

$$x=\frac{-2±\sqrt{868}}{2\times 36}$$

Tuhia te pūtakerua o te 868.

$$x=\frac{-2±2\sqrt{217}}{2\times 36}$$

Whakareatia 2 ki te 36.

$$x=\frac{-2±2\sqrt{217}}{72}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{217}}{72} ina he tāpiri te ±. Tāpiri -2 ki te 2\sqrt{217}.

$$x=\frac{2\sqrt{217}-2}{72}$$

Whakawehe -2+2\sqrt{217} ki te 72.

$$x=\frac{\sqrt{217}-1}{36}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{217}}{72} ina he tango te ±. Tango 2\sqrt{217} mai i -2.

$$x=\frac{-2\sqrt{217}-2}{72}$$

Whakawehe -2-2\sqrt{217} ki te 72.

$$x=\frac{-\sqrt{217}-1}{36}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{217}-1}{36} x=\frac{-\sqrt{217}-1}{36}$$

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.

$$36x^{2}+2x-6=0$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$36x^{2}+2x-6-\left(-6\right)=-\left(-6\right)$$

Mā te tango i te -6 i a ia ake anō ka toe ko te 0.

$$36x^{2}+2x=-\left(-6\right)$$

Tango -6 mai i 0.

$$36x^{2}+2x=6$$

Whakawehea ngā taha e rua ki te 36.

$$\frac{36x^{2}+2x}{36}=\frac{6}{36}$$

Mā te whakawehe ki te 36 ka wetekia te whakareanga ki te 36.

$$x^{2}+\frac{2}{36}x=\frac{6}{36}$$

Whakahekea te hautanga \frac{2}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}+\frac{1}{18}x=\frac{6}{36}$$

Whakahekea te hautanga \frac{6}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x^{2}+\frac{1}{18}x=\frac{1}{6}$$

Whakawehea te \frac{1}{18}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{36}. Nā, tāpiria te pūrua o te \frac{1}{36} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{1}{18}x+\left(\frac{1}{36}\right)^{2}=\frac{1}{6}+\left(\frac{1}{36}\right)^{2}$$

Pūruatia \frac{1}{36} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{1}{18}x+\frac{1}{1296}=\frac{1}{6}+\frac{1}{1296}$$

Tāpiri \frac{1}{6} ki te \frac{1}{1296} 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.

$$x^{2}+\frac{1}{18}x+\frac{1}{1296}=\frac{217}{1296}$$

Tauwehea x^{2}+\frac{1}{18}x+\frac{1}{1296}. 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}.

$$\left(x+\frac{1}{36}\right)^{2}=\frac{217}{1296}$$

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

$$\sqrt{\left(x+\frac{1}{36}\right)^{2}}=\sqrt{\frac{217}{1296}}$$

Whakarūnātia.

$$x+\frac{1}{36}=\frac{\sqrt{217}}{36} x+\frac{1}{36}=-\frac{\sqrt{217}}{36}$$

Me tango \frac{1}{36} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{217}-1}{36} x=\frac{-\sqrt{217}-1}{36}$$