Whakaoti i te -96/x/1-x=40.5

$$\frac{ \frac{ -96 }{ x } }{ 1-x } =40.5$$

Whakaoti mō x

$$x=\frac{\sqrt{849}}{18}+0.5\approx 2.118755809$$

$$x=-\frac{\sqrt{849}}{18}+0.5\approx -1.118755809$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+1.

$$\frac{-96}{x}=40.5\left(-x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 40.5 ki te -x+1.

$$\frac{-96}{x}=-40.5x+40.5$$

Me tāpiri te 40.5x ki ngā taha e rua.

$$\frac{-96}{x}+40.5x=40.5$$

Tangohia te 40.5 mai i ngā taha e rua.

$$\frac{-96}{x}+40.5x-40.5=0$$

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.

$$-96+40.5xx+x\left(-40.5\right)=0$$

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

$$-96+40.5x^{2}+x\left(-40.5\right)=0$$

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.

$$40.5x^{2}-40.5x-96=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 40.5 mō a, -40.5 mō b, me -96 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-40.5\right)±\sqrt{\left(-40.5\right)^{2}-4\times 40.5\left(-96\right)}}{2\times 40.5}$$

Pūruatia -40.5 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-40.5\right)±\sqrt{1640.25-4\times 40.5\left(-96\right)}}{2\times 40.5}$$

Whakareatia -4 ki te 40.5.

$$x=\frac{-\left(-40.5\right)±\sqrt{1640.25-162\left(-96\right)}}{2\times 40.5}$$

Whakareatia -162 ki te -96.

$$x=\frac{-\left(-40.5\right)±\sqrt{1640.25+15552}}{2\times 40.5}$$

Tāpiri 1640.25 ki te 15552.

$$x=\frac{-\left(-40.5\right)±\sqrt{17192.25}}{2\times 40.5}$$

Tuhia te pūtakerua o te 17192.25.

$$x=\frac{-\left(-40.5\right)±\frac{9\sqrt{849}}{2}}{2\times 40.5}$$

Ko te tauaro o -40.5 ko 40.5.

$$x=\frac{40.5±\frac{9\sqrt{849}}{2}}{2\times 40.5}$$

Whakareatia 2 ki te 40.5.

$$x=\frac{40.5±\frac{9\sqrt{849}}{2}}{81}$$

Nā, me whakaoti te whārite x=\frac{40.5±\frac{9\sqrt{849}}{2}}{81} ina he tāpiri te ±. Tāpiri 40.5 ki te \frac{9\sqrt{849}}{2}.

$$x=\frac{9\sqrt{849}+81}{2\times 81}$$

Whakawehe \frac{81+9\sqrt{849}}{2} ki te 81.

$$x=\frac{\sqrt{849}}{18}+\frac{1}{2}$$

Nā, me whakaoti te whārite x=\frac{40.5±\frac{9\sqrt{849}}{2}}{81} ina he tango te ±. Tango \frac{9\sqrt{849}}{2} mai i 40.5.

$$x=\frac{81-9\sqrt{849}}{2\times 81}$$

Whakawehe \frac{81-9\sqrt{849}}{2} ki te 81.

$$x=-\frac{\sqrt{849}}{18}+\frac{1}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{849}}{18}+\frac{1}{2} x=-\frac{\sqrt{849}}{18}+\frac{1}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+1.

$$\frac{-96}{x}=40.5\left(-x+1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 40.5 ki te -x+1.

$$\frac{-96}{x}=-40.5x+40.5$$

Me tāpiri te 40.5x ki ngā taha e rua.

$$\frac{-96}{x}+40.5x=40.5$$

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.

$$-96+40.5xx=40.5x$$

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

$$-96+40.5x^{2}=40.5x$$

Tangohia te 40.5x mai i ngā taha e rua.

$$-96+40.5x^{2}-40.5x=0$$

Me tāpiri te 96 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$40.5x^{2}-40.5x=96$$

Whakawehea ngā taha e rua o te whārite ki te 40.5, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{40.5x^{2}-40.5x}{40.5}=\frac{96}{40.5}$$

Mā te whakawehe ki te 40.5 ka wetekia te whakareanga ki te 40.5.

$$x^{2}+\left(-\frac{40.5}{40.5}\right)x=\frac{96}{40.5}$$

Whakawehe -40.5 ki te 40.5 mā te whakarea -40.5 ki te tau huripoki o 40.5.

$$x^{2}-x=\frac{96}{40.5}$$

Whakawehe 96 ki te 40.5 mā te whakarea 96 ki te tau huripoki o 40.5.

$$x^{2}-x=\frac{64}{27}$$

Whakawehea te -1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{2}. Nā, tāpiria te pūrua o te -\frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=\frac{64}{27}+\left(-\frac{1}{2}\right)^{2}$$

Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-x+\frac{1}{4}=\frac{64}{27}+\frac{1}{4}$$

Tāpiri \frac{64}{27} ki te \frac{1}{4} 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.

$$x^{2}-x+\frac{1}{4}=\frac{283}{108}$$

Tauwehea x^{2}-x+\frac{1}{4}. 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}.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{283}{108}$$

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

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{283}{108}}$$

Whakarūnātia.

$$x-\frac{1}{2}=\frac{\sqrt{849}}{18} x-\frac{1}{2}=-\frac{\sqrt{849}}{18}$$

Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{849}}{18}+\frac{1}{2} x=-\frac{\sqrt{849}}{18}+\frac{1}{2}$$