Whakaoti i te 7200(1+0.2)/x-7200/x+4=200

$$\frac { 7200 ( 1 + 0.2 ) } { x } - \frac { 7200 } { x + 4 } = 200$$

Whakaoti mō x

$$x = \frac{4 \sqrt{274} + 8}{5} \approx 14.842356286$$

$$x=\frac{8-4\sqrt{274}}{5}\approx -11.642356286$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -4,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x+4\right), arā, te tauraro pātahi he tino iti rawa te kitea o x,x+4.

$$\left(x+4\right)\times 7200\left(1+0.2\right)-x\times 7200=200x\left(x+4\right)$$

Tāpirihia te 1 ki te 0.2, ka 1.2.

$$\left(x+4\right)\times 7200\times 1.2-x\times 7200=200x\left(x+4\right)$$

Whakareatia te 7200 ki te 1.2, ka 8640.

$$\left(x+4\right)\times 8640-x\times 7200=200x\left(x+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+4 ki te 8640.

$$8640x+34560-x\times 7200=200x\left(x+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 200x ki te x+4.

$$8640x+34560-x\times 7200=200x^{2}+800x$$

Tangohia te 200x^{2} mai i ngā taha e rua.

$$8640x+34560-x\times 7200-200x^{2}=800x$$

Tangohia te 800x mai i ngā taha e rua.

$$8640x+34560-x\times 7200-200x^{2}-800x=0$$

Pahekotia te 8640x me -800x, ka 7840x.

$$7840x+34560-x\times 7200-200x^{2}=0$$

Whakareatia te -1 ki te 7200, ka -7200.

$$7840x+34560-7200x-200x^{2}=0$$

Pahekotia te 7840x me -7200x, ka 640x.

$$640x+34560-200x^{2}=0$$

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.

$$-200x^{2}+640x+34560=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -200 mō a, 640 mō b, me 34560 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-640±\sqrt{640^{2}-4\left(-200\right)\times 34560}}{2\left(-200\right)}$$

Pūrua 640.

$$x=\frac{-640±\sqrt{409600-4\left(-200\right)\times 34560}}{2\left(-200\right)}$$

Whakareatia -4 ki te -200.

$$x=\frac{-640±\sqrt{409600+800\times 34560}}{2\left(-200\right)}$$

Whakareatia 800 ki te 34560.

$$x=\frac{-640±\sqrt{409600+27648000}}{2\left(-200\right)}$$

Tāpiri 409600 ki te 27648000.

$$x=\frac{-640±\sqrt{28057600}}{2\left(-200\right)}$$

Tuhia te pūtakerua o te 28057600.

$$x=\frac{-640±320\sqrt{274}}{2\left(-200\right)}$$

Whakareatia 2 ki te -200.

$$x=\frac{-640±320\sqrt{274}}{-400}$$

Nā, me whakaoti te whārite x=\frac{-640±320\sqrt{274}}{-400} ina he tāpiri te ±. Tāpiri -640 ki te 320\sqrt{274}.

$$x=\frac{320\sqrt{274}-640}{-400}$$

Whakawehe -640+320\sqrt{274} ki te -400.

$$x=\frac{8-4\sqrt{274}}{5}$$

Nā, me whakaoti te whārite x=\frac{-640±320\sqrt{274}}{-400} ina he tango te ±. Tango 320\sqrt{274} mai i -640.

$$x=\frac{-320\sqrt{274}-640}{-400}$$

Whakawehe -640-320\sqrt{274} ki te -400.

$$x=\frac{4\sqrt{274}+8}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{8-4\sqrt{274}}{5} x=\frac{4\sqrt{274}+8}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -4,0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te x\left(x+4\right), arā, te tauraro pātahi he tino iti rawa te kitea o x,x+4.

$$\left(x+4\right)\times 7200\left(1+0.2\right)-x\times 7200=200x\left(x+4\right)$$

Tāpirihia te 1 ki te 0.2, ka 1.2.

$$\left(x+4\right)\times 7200\times 1.2-x\times 7200=200x\left(x+4\right)$$

Whakareatia te 7200 ki te 1.2, ka 8640.

$$\left(x+4\right)\times 8640-x\times 7200=200x\left(x+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+4 ki te 8640.

$$8640x+34560-x\times 7200=200x\left(x+4\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 200x ki te x+4.

$$8640x+34560-x\times 7200=200x^{2}+800x$$

Tangohia te 200x^{2} mai i ngā taha e rua.

$$8640x+34560-x\times 7200-200x^{2}=800x$$

Tangohia te 800x mai i ngā taha e rua.

$$8640x+34560-x\times 7200-200x^{2}-800x=0$$

Pahekotia te 8640x me -800x, ka 7840x.

$$7840x+34560-x\times 7200-200x^{2}=0$$

Tangohia te 34560 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$7840x-x\times 7200-200x^{2}=-34560$$

Whakareatia te -1 ki te 7200, ka -7200.

$$7840x-7200x-200x^{2}=-34560$$

Pahekotia te 7840x me -7200x, ka 640x.

$$640x-200x^{2}=-34560$$

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.

$$-200x^{2}+640x=-34560$$

Whakawehea ngā taha e rua ki te -200.

$$\frac{-200x^{2}+640x}{-200}=-\frac{34560}{-200}$$

Mā te whakawehe ki te -200 ka wetekia te whakareanga ki te -200.

$$x^{2}+\frac{640}{-200}x=-\frac{34560}{-200}$$

Whakahekea te hautanga \frac{640}{-200} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 40.

$$x^{2}-\frac{16}{5}x=-\frac{34560}{-200}$$

Whakahekea te hautanga \frac{-34560}{-200} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 40.

$$x^{2}-\frac{16}{5}x=\frac{864}{5}$$

Whakawehea te -\frac{16}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{8}{5}. Nā, tāpiria te pūrua o te -\frac{8}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{16}{5}x+\left(-\frac{8}{5}\right)^{2}=\frac{864}{5}+\left(-\frac{8}{5}\right)^{2}$$

Pūruatia -\frac{8}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{16}{5}x+\frac{64}{25}=\frac{864}{5}+\frac{64}{25}$$

Tāpiri \frac{864}{5} ki te \frac{64}{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.

$$x^{2}-\frac{16}{5}x+\frac{64}{25}=\frac{4384}{25}$$

Tauwehea x^{2}-\frac{16}{5}x+\frac{64}{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}.

$$\left(x-\frac{8}{5}\right)^{2}=\frac{4384}{25}$$

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

$$\sqrt{\left(x-\frac{8}{5}\right)^{2}}=\sqrt{\frac{4384}{25}}$$

Whakarūnātia.

$$x-\frac{8}{5}=\frac{4\sqrt{274}}{5} x-\frac{8}{5}=-\frac{4\sqrt{274}}{5}$$

Me tāpiri \frac{8}{5} ki ngā taha e rua o te whārite.

$$x=\frac{4\sqrt{274}+8}{5} x=\frac{8-4\sqrt{274}}{5}$$