Whakaoti i te 5-x/4*10^6=96x-x^2

$$\frac { 5 - x } { 4 \times 10 ^ { 6 } } = 96 x - x ^ { 2 }$$

Whakaoti mō x

$$x = \frac{\sqrt{147456000688000001} + 384000001}{8000000} \approx 96.000000237$$

$$x=\frac{384000001-\sqrt{147456000688000001}}{8000000}\approx 0.000000013$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 10 mā te pū o 6, kia riro ko 1000000.

$$\frac{5-x}{4\times 1000000}=96x-x^{2}$$

Whakareatia te 4 ki te 1000000, ka 4000000.

$$\frac{5-x}{4000000}=96x-x^{2}$$

Whakawehea ia wā o 5-x ki te 4000000, kia riro ko \frac{1}{800000}-\frac{1}{4000000}x.

$$\frac{1}{800000}-\frac{1}{4000000}x=96x-x^{2}$$

Tangohia te 96x mai i ngā taha e rua.

$$\frac{1}{800000}-\frac{1}{4000000}x-96x=-x^{2}$$

Pahekotia te -\frac{1}{4000000}x me -96x, ka -\frac{384000001}{4000000}x.

$$\frac{1}{800000}-\frac{384000001}{4000000}x=-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$\frac{1}{800000}-\frac{384000001}{4000000}x+x^{2}=0$$

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.

$$x^{2}-\frac{384000001}{4000000}x+\frac{1}{800000}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -\frac{384000001}{4000000} mō b, me \frac{1}{800000} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\sqrt{\left(-\frac{384000001}{4000000}\right)^{2}-4\times \frac{1}{800000}}}{2}$$

Pūruatia -\frac{384000001}{4000000} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\sqrt{\frac{147456000768000001}{16000000000000}-4\times \frac{1}{800000}}}{2}$$

Whakareatia -4 ki te \frac{1}{800000}.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\sqrt{\frac{147456000768000001}{16000000000000}-\frac{1}{200000}}}{2}$$

Tāpiri \frac{147456000768000001}{16000000000000} ki te -\frac{1}{200000} 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.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\sqrt{\frac{147456000688000001}{16000000000000}}}{2}$$

Tuhia te pūtakerua o te \frac{147456000688000001}{16000000000000}.

$$x=\frac{-\left(-\frac{384000001}{4000000}\right)±\frac{\sqrt{147456000688000001}}{4000000}}{2}$$

Ko te tauaro o -\frac{384000001}{4000000} ko \frac{384000001}{4000000}.

$$x=\frac{\frac{384000001}{4000000}±\frac{\sqrt{147456000688000001}}{4000000}}{2}$$

Nā, me whakaoti te whārite x=\frac{\frac{384000001}{4000000}±\frac{\sqrt{147456000688000001}}{4000000}}{2} ina he tāpiri te ±. Tāpiri \frac{384000001}{4000000} ki te \frac{\sqrt{147456000688000001}}{4000000}.

$$x=\frac{\sqrt{147456000688000001}[phone]}{2\times 4000000}$$

Whakawehe \frac{384000001+\sqrt{147456000688000001}}{4000000} ki te 2.

$$x=\frac{\sqrt{147456000688000001}[phone]}{8000000}$$

Nā, me whakaoti te whārite x=\frac{\frac{384000001}{4000000}±\frac{\sqrt{147456000688000001}}{4000000}}{2} ina he tango te ±. Tango \frac{\sqrt{147456000688000001}}{4000000} mai i \frac{384000001}{4000000}.

$$x=\frac{384000001-\sqrt{147456000688000001}}{2\times 4000000}$$

Whakawehe \frac{384000001-\sqrt{147456000688000001}}{4000000} ki te 2.

$$x=\frac{384000001-\sqrt{147456000688000001}}{8000000}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{147456000688000001}[phone]}{8000000} x=\frac{384000001-\sqrt{147456000688000001}}{8000000}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tātaihia te 10 mā te pū o 6, kia riro ko 1000000.

$$\frac{5-x}{4\times 1000000}=96x-x^{2}$$

Whakareatia te 4 ki te 1000000, ka 4000000.

$$\frac{5-x}{4000000}=96x-x^{2}$$

Whakawehea ia wā o 5-x ki te 4000000, kia riro ko \frac{1}{800000}-\frac{1}{4000000}x.

$$\frac{1}{800000}-\frac{1}{4000000}x=96x-x^{2}$$

Tangohia te 96x mai i ngā taha e rua.

$$\frac{1}{800000}-\frac{1}{4000000}x-96x=-x^{2}$$

Pahekotia te -\frac{1}{4000000}x me -96x, ka -\frac{384000001}{4000000}x.

$$\frac{1}{800000}-\frac{384000001}{4000000}x=-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$\frac{1}{800000}-\frac{384000001}{4000000}x+x^{2}=0$$

Tangohia te \frac{1}{800000} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-\frac{384000001}{4000000}x+x^{2}=-\frac{1}{800000}$$

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.

$$x^{2}-\frac{384000001}{4000000}x=-\frac{1}{800000}$$

Whakawehea te -\frac{384000001}{4000000}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{384000001}{8000000}. Nā, tāpiria te pūrua o te -\frac{384000001}{8000000} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{384000001}{4000000}x+\left(-\frac{384000001}{8000000}\right)^{2}=-\frac{1}{800000}+\left(-\frac{384000001}{8000000}\right)^{2}$$

Pūruatia -\frac{384000001}{8000000} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{384000001}{4000000}x+\frac{147456000768000001}{64000000000000}=-\frac{1}{800000}+\frac{147456000768000001}{64000000000000}$$

Tāpiri -\frac{1}{800000} ki te \frac{147456000768000001}{64000000000000} 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.

$$x^{2}-\frac{384000001}{4000000}x+\frac{147456000768000001}{64000000000000}=\frac{147456000688000001}{64000000000000}$$

Tauwehea x^{2}-\frac{384000001}{4000000}x+\frac{147456000768000001}{64000000000000}. 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}.

$$\left(x-\frac{384000001}{8000000}\right)^{2}=\frac{147456000688000001}{64000000000000}$$

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

$$\sqrt{\left(x-\frac{384000001}{8000000}\right)^{2}}=\sqrt{\frac{147456000688000001}{64000000000000}}$$

Whakarūnātia.

$$x-\frac{384000001}{8000000}=\frac{\sqrt{147456000688000001}}{8000000} x-\frac{384000001}{8000000}=-\frac{\sqrt{147456000688000001}}{8000000}$$

Me tāpiri \frac{384000001}{8000000} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{147456000688000001}[phone]}{8000000} x=\frac{384000001-\sqrt{147456000688000001}}{8000000}$$