Whakaoti i te 2.25*9.8*1000*12*(1+0.576divx)+1000000divx=2000000

$$2.25 \times 9.8 \times 1000 \times 12 \times (1+0.576 \div x)+1000000 \div x=2000000$$

Whakaoti mō x

$$x=\frac{720256}{1084625}\approx 0.664059929$$

Ngā Upane Whakamahi Tauwehe

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

$$2.25\times 9.8\times 1000\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Whakareatia te 2.25 ki te 9.8, ka 22.05.

$$22.05\times 1000\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Whakareatia te 22.05 ki te 1000, ka 22050.

$$22050\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Whakareatia te 22050 ki te 12, ka 264600.

$$264600\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 264600 ki te 1+\frac{0.576}{x}.

$$\left(264600+264600\times \frac{0.576}{x}\right)x+1000000=2000000x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 264600+264600\times \frac{0.576}{x} ki te x.

$$264600x+264600\times \frac{0.576}{x}x+1000000=2000000x$$

Tangohia te 2000000x mai i ngā taha e rua.

$$264600x+264600\times \frac{0.576}{x}x+1000000-2000000x=0$$

Pahekotia te 264600x me -2000000x, ka -1735400x.

$$-1735400x+264600\times \frac{0.576}{x}x+1000000=0$$

Tangohia te 1000000 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-1735400x+264600\times \frac{0.576}{x}x=-1000000$$

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

$$-1735400xx+264600\times 0.576x=-1000000x$$

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

$$-1735400x^{2}+264600\times 0.576x=-1000000x$$

Whakareatia te 264600 ki te 0.576, ka 152409.6.

$$-1735400x^{2}+152409.6x=-1000000x$$

Me tāpiri te 1000000x ki ngā taha e rua.

$$-1735400x^{2}+152409.6x+1000000x=0$$

Pahekotia te 152409.6x me 1000000x, ka 1152409.6x.

$$-1735400x^{2}+1152409.6x=0$$

Tauwehea te x.

$$x\left(-1735400x+1152409.6\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -1735400x+1152409.6=0.

$$x=0 x=\frac{720256}{1084625}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{720256}{1084625}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$2.25\times 9.8\times 1000\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Whakareatia te 2.25 ki te 9.8, ka 22.05.

$$22.05\times 1000\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Whakareatia te 22.05 ki te 1000, ka 22050.

$$22050\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Whakareatia te 22050 ki te 12, ka 264600.

$$264600\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 264600 ki te 1+\frac{0.576}{x}.

$$\left(264600+264600\times \frac{0.576}{x}\right)x+1000000=2000000x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 264600+264600\times \frac{0.576}{x} ki te x.

$$264600x+264600\times \frac{0.576}{x}x+1000000=2000000x$$

Tangohia te 2000000x mai i ngā taha e rua.

$$264600x+264600\times \frac{0.576}{x}x+1000000-2000000x=0$$

Pahekotia te 264600x me -2000000x, ka -1735400x.

$$-1735400x+264600\times \frac{0.576}{x}x+1000000=0$$

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

$$-1735400xx+264600\times 0.576x+x\times 1000000=0$$

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

$$-1735400x^{2}+264600\times 0.576x+x\times 1000000=0$$

Whakareatia te 264600 ki te 0.576, ka 152409.6.

$$-1735400x^{2}+152409.6x+x\times 1000000=0$$

Pahekotia te 152409.6x me x\times 1000000, ka 1152409.6x.

$$-1735400x^{2}+1152409.6x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1735400 mō a, 1152409.6 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1152409.6±\sqrt{1152409.6^{2}}}{2\left(-1735400\right)}$$

Tuhia te pūtakerua o te 1152409.6^{2}.

$$x=\frac{-1152409.6±\frac{5762048}{5}}{2\left(-1735400\right)}$$

Whakareatia 2 ki te -1735400.

$$x=\frac{-1152409.6±\frac{5762048}{5}}{-3470800}$$

Nā, me whakaoti te whārite x=\frac{-1152409.6±\frac{5762048}{5}}{-3470800} ina he tāpiri te ±. Tāpiri -1152409.6 ki te \frac{5762048}{5} 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.

$$x=\frac{0}{-3470800}$$

Whakawehe 0 ki te -3470800.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-1152409.6±\frac{5762048}{5}}{-3470800} ina he tango te ±. Tango \frac{5762048}{5} mai i -1152409.6 mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=-\frac{\frac{11524096}{5}}{-3470800}$$

Whakawehe -\frac{11524096}{5} ki te -3470800.

$$x=\frac{720256}{1084625}$$

Kua oti te whārite te whakatau.

$$x=0 x=\frac{720256}{1084625}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{720256}{1084625}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$2.25\times 9.8\times 1000\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Whakareatia te 2.25 ki te 9.8, ka 22.05.

$$22.05\times 1000\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Whakareatia te 22.05 ki te 1000, ka 22050.

$$22050\times 12\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Whakareatia te 22050 ki te 12, ka 264600.

$$264600\left(1+\frac{0.576}{x}\right)x+1000000=2000000x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 264600 ki te 1+\frac{0.576}{x}.

$$\left(264600+264600\times \frac{0.576}{x}\right)x+1000000=2000000x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 264600+264600\times \frac{0.576}{x} ki te x.

$$264600x+264600\times \frac{0.576}{x}x+1000000=2000000x$$

Tangohia te 2000000x mai i ngā taha e rua.

$$264600x+264600\times \frac{0.576}{x}x+1000000-2000000x=0$$

Pahekotia te 264600x me -2000000x, ka -1735400x.

$$-1735400x+264600\times \frac{0.576}{x}x+1000000=0$$

Tangohia te 1000000 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-1735400x+264600\times \frac{0.576}{x}x=-1000000$$

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

$$-1735400xx+264600\times 0.576x=-1000000x$$

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

$$-1735400x^{2}+264600\times 0.576x=-1000000x$$

Whakareatia te 264600 ki te 0.576, ka 152409.6.

$$-1735400x^{2}+152409.6x=-1000000x$$

Me tāpiri te 1000000x ki ngā taha e rua.

$$-1735400x^{2}+152409.6x+1000000x=0$$

Pahekotia te 152409.6x me 1000000x, ka 1152409.6x.

$$-1735400x^{2}+1152409.6x=0$$

Whakawehea ngā taha e rua ki te -1735400.

$$\frac{-1735400x^{2}+1152409.6x}{-1735400}=\frac{0}{-1735400}$$

Mā te whakawehe ki te -1735400 ka wetekia te whakareanga ki te -1735400.

$$x^{2}+\frac{1152409.6}{-1735400}x=\frac{0}{-1735400}$$

Whakawehe 1152409.6 ki te -1735400.

$$x^{2}-\frac{720256}{1084625}x=\frac{0}{-1735400}$$

Whakawehe 0 ki te -1735400.

$$x^{2}-\frac{720256}{1084625}x=0$$

Whakawehea te -\frac{720256}{1084625}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{360128}{1084625}. Nā, tāpiria te pūrua o te -\frac{360128}{1084625} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{720256}{1084625}x+\left(-\frac{360128}{1084625}\right)^{2}=\left(-\frac{360128}{1084625}\right)^{2}$$

Pūruatia -\frac{360128}{1084625} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{720256}{1084625}x+\frac{129692176384}{1176411390625}=\frac{129692176384}{1176411390625}$$

Tauwehea x^{2}-\frac{720256}{1084625}x+\frac{129692176384}{1176411390625}. 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}.

$$\left(x-\frac{360128}{1084625}\right)^{2}=\frac{129692176384}{1176411390625}$$

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

$$\sqrt{\left(x-\frac{360128}{1084625}\right)^{2}}=\sqrt{\frac{129692176384}{1176411390625}}$$

Whakarūnātia.

$$x-\frac{360128}{1084625}=\frac{360128}{1084625} x-\frac{360128}{1084625}=-\frac{360128}{1084625}$$

Me tāpiri \frac{360128}{1084625} ki ngā taha e rua o te whārite.

$$x=\frac{720256}{1084625} x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{720256}{1084625}$$