Whakaoti i te 50/17*9800+34*9800h=26500(h^2-8875^2)

$$\frac { 50 } { 17 } \times 9800 + 34 \times 9800 h = 26500 ( h ^ { 2 } - 8875 ^ { 2 } )$$

Whakaoti mō h

$$h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}\approx 8881.289080421$$

$$h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}\approx -8868.715495515$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te \frac{50}{17} ki te 9800, ka \frac{490000}{17}.

$$\frac{490000}{17}+34\times 9800h=26500\left(h^{2}-8875^{2}\right)$$

Whakareatia te 34 ki te 9800, ka 333200.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-8875^{2}\right)$$

Tātaihia te 8875 mā te pū o 2, kia riro ko 78765625.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-78765625\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 26500 ki te h^{2}-78765625.

$$\frac{490000}{17}+333200h=26500h^{2}-2087289062500$$

Tangohia te 26500h^{2} mai i ngā taha e rua.

$$\frac{490000}{17}+333200h-26500h^{2}=-2087289062500$$

Me tāpiri te 2087289062500 ki ngā taha e rua.

$$\frac{490000}{17}+333200h-26500h^{2}[phone]=0$$

Tāpirihia te \frac{490000}{17} ki te 2087289062500, ka \frac{35483914552500}{17}.

$$\frac{35483914552500}{17}+333200h-26500h^{2}=0$$

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.

$$-26500h^{2}+333200h+\frac{35483914552500}{17}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -26500 mō a, 333200 mō b, me \frac{35483914552500}{17} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{-333200±\sqrt{333200^{2}-4\left(-26500\right)\times \frac{35483914552500}{17}}}{2\left(-26500\right)}$$

Pūrua 333200.

$$h=\frac{-333200±\sqrt{111022240000-4\left(-26500\right)\times \frac{35483914552500}{17}}}{2\left(-26500\right)}$$

Whakareatia -4 ki te -26500.

$$h=\frac{-333200±\sqrt{111022240000+106000\times \frac{35483914552500}{17}}}{2\left(-26500\right)}$$

Whakareatia 106000 ki te \frac{35483914552500}{17}.

$$h=\frac{-333200±\sqrt{111022240000+\frac{3761294942565000000}{17}}}{2\left(-26500\right)}$$

Tāpiri 111022240000 ki te \frac{3761294942565000000}{17}.

$$h=\frac{-333200±\sqrt{\frac{3761296829943080000}{17}}}{2\left(-26500\right)}$$

Tuhia te pūtakerua o te \frac{3761296829943080000}{17}.

$$h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{2\left(-26500\right)}$$

Whakareatia 2 ki te -26500.

$$h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{-53000}$$

Nā, me whakaoti te whārite h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{-53000} ina he tāpiri te ±. Tāpiri -333200 ki te \frac{200\sqrt{1598551152725809}}{17}.

$$h=\frac{\frac{200\sqrt{1598551152725809}}{17}-333200}{-53000}$$

Whakawehe -333200+\frac{200\sqrt{1598551152725809}}{17} ki te -53000.

$$h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$

Nā, me whakaoti te whārite h=\frac{-333200±\frac{200\sqrt{1598551152725809}}{17}}{-53000} ina he tango te ±. Tango \frac{200\sqrt{1598551152725809}}{17} mai i -333200.

$$h=\frac{-\frac{200\sqrt{1598551152725809}}{17}-333200}{-53000}$$

Whakawehe -333200-\frac{200\sqrt{1598551152725809}}{17} ki te -53000.

$$h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$

Kua oti te whārite te whakatau.

$$h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265} h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te \frac{50}{17} ki te 9800, ka \frac{490000}{17}.

$$\frac{490000}{17}+34\times 9800h=26500\left(h^{2}-8875^{2}\right)$$

Whakareatia te 34 ki te 9800, ka 333200.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-8875^{2}\right)$$

Tātaihia te 8875 mā te pū o 2, kia riro ko 78765625.

$$\frac{490000}{17}+333200h=26500\left(h^{2}-78765625\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 26500 ki te h^{2}-78765625.

$$\frac{490000}{17}+333200h=26500h^{2}-2087289062500$$

Tangohia te 26500h^{2} mai i ngā taha e rua.

$$\frac{490000}{17}+333200h-26500h^{2}=-2087289062500$$

Tangohia te \frac{490000}{17} mai i ngā taha e rua.

$$333200h-26500h^{2}=-2087289062500-\frac{490000}{17}$$

Tangohia te \frac{490000}{17} i te -2087289062500, ka -\frac{35483914552500}{17}.

$$333200h-26500h^{2}=-\frac{35483914552500}{17}$$

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.

$$-26500h^{2}+333200h=-\frac{35483914552500}{17}$$

Whakawehea ngā taha e rua ki te -26500.

$$\frac{-26500h^{2}+333200h}{-26500}=-\frac{\frac{35483914552500}{17}}{-26500}$$

Mā te whakawehe ki te -26500 ka wetekia te whakareanga ki te -26500.

$$h^{2}+\frac{333200}{-26500}h=-\frac{\frac{35483914552500}{17}}{-26500}$$

Whakahekea te hautanga \frac{333200}{-26500} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 100.

$$h^{2}-\frac{3332}{265}h=-\frac{\frac{35483914552500}{17}}{-26500}$$

Whakawehe -\frac{35483914552500}{17} ki te -26500.

$$h^{2}-\frac{3332}{265}h=\frac{70967829105}{901}$$

Whakawehea te -\frac{3332}{265}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1666}{265}. Nā, tāpiria te pūrua o te -\frac{1666}{265} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$h^{2}-\frac{3332}{265}h+\left(-\frac{1666}{265}\right)^{2}=\frac{70967829105}{901}+\left(-\frac{1666}{265}\right)^{2}$$

Pūruatia -\frac{1666}{265} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$h^{2}-\frac{3332}{265}h+\frac{2775556}{70225}=\frac{70967829105}{901}+\frac{2775556}{70225}$$

Tāpiri \frac{70967829105}{901} ki te \frac{2775556}{70225} 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.

$$h^{2}-\frac{3332}{265}h+\frac{2775556}{70225}=\frac{94032420748577}{1193825}$$

Tauwehea h^{2}-\frac{3332}{265}h+\frac{2775556}{70225}. 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}.

$$\left(h-\frac{1666}{265}\right)^{2}=\frac{94032420748577}{1193825}$$

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

$$\sqrt{\left(h-\frac{1666}{265}\right)^{2}}=\sqrt{\frac{94032420748577}{1193825}}$$

Whakarūnātia.

$$h-\frac{1666}{265}=\frac{\sqrt{1598551152725809}}{4505} h-\frac{1666}{265}=-\frac{\sqrt{1598551152725809}}{4505}$$

Me tāpiri \frac{1666}{265} ki ngā taha e rua o te whārite.

$$h=\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265} h=-\frac{\sqrt{1598551152725809}}{4505}+\frac{1666}{265}$$