Whakaoti i te 4183.92+2*78*9.8x=6.5*10^4quadx^2

$$4183.92 + 2 \times 78 \times 9.8 x = 6.5 \times 10 ^ { 4 } \quad x ^ { 2 }$$

Whakaoti mō x

$$x=\frac{3\sqrt{1119901}+147}{12500}\approx 0.2657409$$

$$x=\frac{147-3\sqrt{1119901}}{12500}\approx -0.2422209$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 2 ki te 78, ka 156.

$$4183.92+156\times 9.8x=6.5\times 10^{4}x^{2}$$

Whakareatia te 156 ki te 9.8, ka 1528.8.

$$4183.92+1528.8x=6.5\times 10^{4}x^{2}$$

Tātaihia te 10 mā te pū o 4, kia riro ko 10000.

$$4183.92+1528.8x=6.5\times 10000x^{2}$$

Whakareatia te 6.5 ki te 10000, ka 65000.

$$4183.92+1528.8x=65000x^{2}$$

Tangohia te 65000x^{2} mai i ngā taha e rua.

$$4183.92+1528.8x-65000x^{2}=0$$

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.

$$-65000x^{2}+1528.8x+4183.92=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -65000 mō a, 1528.8 mō b, me 4183.92 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1528.8±\sqrt{1528.8^{2}-4\left(-65000\right)\times 4183.92}}{2\left(-65000\right)}$$

Pūruatia 1528.8 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-1528.8±\sqrt{2337229.44-4\left(-65000\right)\times 4183.92}}{2\left(-65000\right)}$$

Whakareatia -4 ki te -65000.

$$x=\frac{-1528.8±\sqrt{2337229.44+260000\times 4183.92}}{2\left(-65000\right)}$$

Whakareatia 260000 ki te 4183.92.

$$x=\frac{-1528.8±\sqrt{2337229.44+1087819200}}{2\left(-65000\right)}$$

Tāpiri 2337229.44 ki te 1087819200.

$$x=\frac{-1528.8±\sqrt{1090156429.44}}{2\left(-65000\right)}$$

Tuhia te pūtakerua o te 1090156429.44.

$$x=\frac{-1528.8±\frac{156\sqrt{1119901}}{5}}{2\left(-65000\right)}$$

Whakareatia 2 ki te -65000.

$$x=\frac{-1528.8±\frac{156\sqrt{1119901}}{5}}{-130000}$$

Nā, me whakaoti te whārite x=\frac{-1528.8±\frac{156\sqrt{1119901}}{5}}{-130000} ina he tāpiri te ±. Tāpiri -1528.8 ki te \frac{156\sqrt{1119901}}{5}.

$$x=\frac{156\sqrt{1119901}-7644}{-130000\times 5}$$

Whakawehe \frac{-7644+156\sqrt{1119901}}{5} ki te -130000.

$$x=\frac{147-3\sqrt{1119901}}{12500}$$

Nā, me whakaoti te whārite x=\frac{-1528.8±\frac{156\sqrt{1119901}}{5}}{-130000} ina he tango te ±. Tango \frac{156\sqrt{1119901}}{5} mai i -1528.8.

$$x=\frac{-156\sqrt{1119901}-7644}{-130000\times 5}$$

Whakawehe \frac{-7644-156\sqrt{1119901}}{5} ki te -130000.

$$x=\frac{3\sqrt{1119901}+147}{12500}$$

Kua oti te whārite te whakatau.

$$x=\frac{147-3\sqrt{1119901}}{12500} x=\frac{3\sqrt{1119901}+147}{12500}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 2 ki te 78, ka 156.

$$4183.92+156\times 9.8x=6.5\times 10^{4}x^{2}$$

Whakareatia te 156 ki te 9.8, ka 1528.8.

$$4183.92+1528.8x=6.5\times 10^{4}x^{2}$$

Tātaihia te 10 mā te pū o 4, kia riro ko 10000.

$$4183.92+1528.8x=6.5\times 10000x^{2}$$

Whakareatia te 6.5 ki te 10000, ka 65000.

$$4183.92+1528.8x=65000x^{2}$$

Tangohia te 65000x^{2} mai i ngā taha e rua.

$$4183.92+1528.8x-65000x^{2}=0$$

Tangohia te 4183.92 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$1528.8x-65000x^{2}=-4183.92$$

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.

$$-65000x^{2}+1528.8x=-4183.92$$

Whakawehea ngā taha e rua ki te -65000.

$$\frac{-65000x^{2}+1528.8x}{-65000}=-\frac{4183.92}{-65000}$$

Mā te whakawehe ki te -65000 ka wetekia te whakareanga ki te -65000.

$$x^{2}+\frac{1528.8}{-65000}x=-\frac{4183.92}{-65000}$$

Whakawehe 1528.8 ki te -65000.

$$x^{2}-0.02352x=-\frac{4183.92}{-65000}$$

Whakawehe -4183.92 ki te -65000.

$$x^{2}-0.02352x=0.064368$$

Whakawehea te -0.02352, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -0.01176. Nā, tāpiria te pūrua o te -0.01176 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-0.02352x+\left(-0.01176\right)^{2}=0.064368+\left(-0.01176\right)^{2}$$

Pūruatia -0.01176 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-0.02352x+0.0001382976=0.064368+0.0001382976$$

Tāpiri 0.064368 ki te 0.0001382976 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.

$$x^{2}-0.02352x+0.0001382976=0.0645062976$$

Tauwehea x^{2}-0.02352x+0.0001382976. 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}.

$$\left(x-0.01176\right)^{2}=0.0645062976$$

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

$$\sqrt{\left(x-0.01176\right)^{2}}=\sqrt{0.0645062976}$$

Whakarūnātia.

$$x-0.01176=\frac{3\sqrt{1119901}}{12500} x-0.01176=-\frac{3\sqrt{1119901}}{12500}$$

Me tāpiri 0.01176 ki ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{1119901}+147}{12500} x=\frac{147-3\sqrt{1119901}}{12500}$$