Whakaoti i te 200+6x^2=80x

$$200 + 6 x ^ { 2 } = 80 x$$

Whakaoti mō x

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

$$x=10$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 80x mai i ngā taha e rua.

$$200+6x^{2}-80x=0$$

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.

$$6x^{2}-80x+200=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, -80 mō b, me 200 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-80\right)±\sqrt{\left(-80\right)^{2}-4\times 6\times 200}}{2\times 6}$$

Pūrua -80.

$$x=\frac{-\left(-80\right)±\sqrt{6400-4\times 6\times 200}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-\left(-80\right)±\sqrt{6400-24\times 200}}{2\times 6}$$

Whakareatia -24 ki te 200.

$$x=\frac{-\left(-80\right)±\sqrt{6400-4800}}{2\times 6}$$

Tāpiri 6400 ki te -4800.

$$x=\frac{-\left(-80\right)±\sqrt{1600}}{2\times 6}$$

Tuhia te pūtakerua o te 1600.

$$x=\frac{-\left(-80\right)±40}{2\times 6}$$

Ko te tauaro o -80 ko 80.

$$x=\frac{80±40}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{80±40}{12}$$

Nā, me whakaoti te whārite x=\frac{80±40}{12} ina he tāpiri te ±. Tāpiri 80 ki te 40.

$$x=\frac{120}{12}$$

Whakawehe 120 ki te 12.

$$x=10$$

Nā, me whakaoti te whārite x=\frac{80±40}{12} ina he tango te ±. Tango 40 mai i 80.

$$x=\frac{40}{12}$$

Whakahekea te hautanga \frac{40}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{10}{3}$$

Kua oti te whārite te whakatau.

$$x=10 x=\frac{10}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 80x mai i ngā taha e rua.

$$200+6x^{2}-80x=0$$

Tangohia te 200 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$6x^{2}-80x=-200$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}-80x}{6}=-\frac{200}{6}$$

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

$$x^{2}+\left(-\frac{80}{6}\right)x=-\frac{200}{6}$$

Whakahekea te hautanga \frac{-80}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{40}{3}x=-\frac{200}{6}$$

Whakahekea te hautanga \frac{-200}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{40}{3}x=-\frac{100}{3}$$

Whakawehea te -\frac{40}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{20}{3}. Nā, tāpiria te pūrua o te -\frac{20}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{40}{3}x+\left(-\frac{20}{3}\right)^{2}=-\frac{100}{3}+\left(-\frac{20}{3}\right)^{2}$$

Pūruatia -\frac{20}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{40}{3}x+\frac{400}{9}=-\frac{100}{3}+\frac{400}{9}$$

Tāpiri -\frac{100}{3} ki te \frac{400}{9} 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.

$$x^{2}-\frac{40}{3}x+\frac{400}{9}=\frac{100}{9}$$

Tauwehea x^{2}-\frac{40}{3}x+\frac{400}{9}. 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}.

$$\left(x-\frac{20}{3}\right)^{2}=\frac{100}{9}$$

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

$$\sqrt{\left(x-\frac{20}{3}\right)^{2}}=\sqrt{\frac{100}{9}}$$

Whakarūnātia.

$$x-\frac{20}{3}=\frac{10}{3} x-\frac{20}{3}=-\frac{10}{3}$$

Me tāpiri \frac{20}{3} ki ngā taha e rua o te whārite.

$$x=10 x=\frac{10}{3}$$