Whakaoti i te E-131.7=68.3:E=

$$E - 131.7 = 68.3 : E =$$

Whakaoti mō E

$$E = \frac{\sqrt{1761809} + 1317}{20} \approx 132.216576678$$

$$E=\frac{1317-\sqrt{1761809}}{20}\approx -0.516576678$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe E ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te E.

$$EE+E\left(-131.7\right)=68.3$$

Whakareatia te E ki te E, ka E^{2}.

$$E^{2}+E\left(-131.7\right)=68.3$$

Tangohia te 68.3 mai i ngā taha e rua.

$$E^{2}+E\left(-131.7\right)-68.3=0$$

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.

$$E^{2}-131.7E-68.3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -131.7 mō b, me -68.3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$E=\frac{-\left(-131.7\right)±\sqrt{\left(-131.7\right)^{2}-4\left(-68.3\right)}}{2}$$

Pūruatia -131.7 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$E=\frac{-\left(-131.7\right)±\sqrt{17344.89-4\left(-68.3\right)}}{2}$$

Whakareatia -4 ki te -68.3.

$$E=\frac{-\left(-131.7\right)±\sqrt{17344.89+273.2}}{2}$$

Tāpiri 17344.89 ki te 273.2 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.

$$E=\frac{-\left(-131.7\right)±\sqrt{17618.09}}{2}$$

Tuhia te pūtakerua o te 17618.09.

$$E=\frac{-\left(-131.7\right)±\frac{\sqrt{1761809}}{10}}{2}$$

Ko te tauaro o -131.7 ko 131.7.

$$E=\frac{131.7±\frac{\sqrt{1761809}}{10}}{2}$$

Nā, me whakaoti te whārite E=\frac{131.7±\frac{\sqrt{1761809}}{10}}{2} ina he tāpiri te ±. Tāpiri 131.7 ki te \frac{\sqrt{1761809}}{10}.

$$E=\frac{\sqrt{1761809}+1317}{2\times 10}$$

Whakawehe \frac{1317+\sqrt{1761809}}{10} ki te 2.

$$E=\frac{\sqrt{1761809}+1317}{20}$$

Nā, me whakaoti te whārite E=\frac{131.7±\frac{\sqrt{1761809}}{10}}{2} ina he tango te ±. Tango \frac{\sqrt{1761809}}{10} mai i 131.7.

$$E=\frac{1317-\sqrt{1761809}}{2\times 10}$$

Whakawehe \frac{1317-\sqrt{1761809}}{10} ki te 2.

$$E=\frac{1317-\sqrt{1761809}}{20}$$

Kua oti te whārite te whakatau.

$$E=\frac{\sqrt{1761809}+1317}{20} E=\frac{1317-\sqrt{1761809}}{20}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe E ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te E.

$$EE+E\left(-131.7\right)=68.3$$

Whakareatia te E ki te E, ka E^{2}.

$$E^{2}+E\left(-131.7\right)=68.3$$

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.

$$E^{2}-131.7E=68.3$$

Whakawehea te -131.7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -65.85. Nā, tāpiria te pūrua o te -65.85 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$E^{2}-131.7E+\left(-65.85\right)^{2}=68.3+\left(-65.85\right)^{2}$$

Pūruatia -65.85 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$E^{2}-131.7E+4336.2225=68.3+4336.2225$$

Tāpiri 68.3 ki te 4336.2225 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.

$$E^{2}-131.7E+4336.2225=4404.5225$$

Tauwehea E^{2}-131.7E+4336.2225. 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}.

$$\left(E-65.85\right)^{2}=4404.5225$$

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

$$\sqrt{\left(E-65.85\right)^{2}}=\sqrt{4404.5225}$$

Whakarūnātia.

$$E-65.85=\frac{\sqrt{1761809}}{20} E-65.85=-\frac{\sqrt{1761809}}{20}$$

Me tāpiri 65.85 ki ngā taha e rua o te whārite.

$$E=\frac{\sqrt{1761809}+1317}{20} E=\frac{1317-\sqrt{1761809}}{20}$$