Whakaoti i te x^2*10div6+6=765-2x

$${ x }^{ 2 } \times 10 \div 6+6=765-2x$$

Whakaoti mō x

$$x = \frac{3 \sqrt{1266} - 3}{5} \approx 20.74853625$$

$$x=\frac{-3\sqrt{1266}-3}{5}\approx -21.94853625$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 6.

$$x^{2}\times 10+36=4590-12x$$

Tangohia te 4590 mai i ngā taha e rua.

$$x^{2}\times 10+36-4590=-12x$$

Tangohia te 4590 i te 36, ka -4554.

$$x^{2}\times 10-4554=-12x$$

Me tāpiri te 12x ki ngā taha e rua.

$$x^{2}\times 10-4554+12x=0$$

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.

$$10x^{2}+12x-4554=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 10 mō a, 12 mō b, me -4554 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\times 10\left(-4554\right)}}{2\times 10}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 10\left(-4554\right)}}{2\times 10}$$

Whakareatia -4 ki te 10.

$$x=\frac{-12±\sqrt{144-40\left(-4554\right)}}{2\times 10}$$

Whakareatia -40 ki te -4554.

$$x=\frac{-12±\sqrt{144+182160}}{2\times 10}$$

Tāpiri 144 ki te 182160.

$$x=\frac{-12±\sqrt{182304}}{2\times 10}$$

Tuhia te pūtakerua o te 182304.

$$x=\frac{-12±12\sqrt{1266}}{2\times 10}$$

Whakareatia 2 ki te 10.

$$x=\frac{-12±12\sqrt{1266}}{20}$$

Nā, me whakaoti te whārite x=\frac{-12±12\sqrt{1266}}{20} ina he tāpiri te ±. Tāpiri -12 ki te 12\sqrt{1266}.

$$x=\frac{12\sqrt{1266}-12}{20}$$

Whakawehe -12+12\sqrt{1266} ki te 20.

$$x=\frac{3\sqrt{1266}-3}{5}$$

Nā, me whakaoti te whārite x=\frac{-12±12\sqrt{1266}}{20} ina he tango te ±. Tango 12\sqrt{1266} mai i -12.

$$x=\frac{-12\sqrt{1266}-12}{20}$$

Whakawehe -12-12\sqrt{1266} ki te 20.

$$x=\frac{-3\sqrt{1266}-3}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{3\sqrt{1266}-3}{5} x=\frac{-3\sqrt{1266}-3}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 6.

$$x^{2}\times 10+36=4590-12x$$

Me tāpiri te 12x ki ngā taha e rua.

$$x^{2}\times 10+36+12x=4590$$

Tangohia te 36 mai i ngā taha e rua.

$$x^{2}\times 10+12x=4590-36$$

Tangohia te 36 i te 4590, ka 4554.

$$x^{2}\times 10+12x=4554$$

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.

$$10x^{2}+12x=4554$$

Whakawehea ngā taha e rua ki te 10.

$$\frac{10x^{2}+12x}{10}=\frac{4554}{10}$$

Mā te whakawehe ki te 10 ka wetekia te whakareanga ki te 10.

$$x^{2}+\frac{12}{10}x=\frac{4554}{10}$$

Whakahekea te hautanga \frac{12}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}+\frac{6}{5}x=\frac{4554}{10}$$

Whakahekea te hautanga \frac{4554}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}+\frac{6}{5}x=\frac{2277}{5}$$

Whakawehea te \frac{6}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{3}{5}. Nā, tāpiria te pūrua o te \frac{3}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{6}{5}x+\left(\frac{3}{5}\right)^{2}=\frac{2277}{5}+\left(\frac{3}{5}\right)^{2}$$

Pūruatia \frac{3}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{6}{5}x+\frac{9}{25}=\frac{2277}{5}+\frac{9}{25}$$

Tāpiri \frac{2277}{5} ki te \frac{9}{25} 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.

$$x^{2}+\frac{6}{5}x+\frac{9}{25}=\frac{11394}{25}$$

Tauwehea x^{2}+\frac{6}{5}x+\frac{9}{25}. 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}.

$$\left(x+\frac{3}{5}\right)^{2}=\frac{11394}{25}$$

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

$$\sqrt{\left(x+\frac{3}{5}\right)^{2}}=\sqrt{\frac{11394}{25}}$$

Whakarūnātia.

$$x+\frac{3}{5}=\frac{3\sqrt{1266}}{5} x+\frac{3}{5}=-\frac{3\sqrt{1266}}{5}$$

Me tango \frac{3}{5} mai i ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{1266}-3}{5} x=\frac{-3\sqrt{1266}-3}{5}$$