Whakaoti i te 185*10^6=143*400left(950-x^2/2right)

$$185 \times { 10 }^{ 6 } = 143 \cdot 400 \left( 950- \frac{ { x }^{ 2 } }{ 2 } \right)$$

Whakaoti mō x (complex solution)

$$x=-\frac{10\sqrt{934219}i}{143}\approx -0-67.590912618i$$

$$x=\frac{10\sqrt{934219}i}{143}\approx 67.590912618i$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$370\times 10^{6}=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

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

$$370\times 1000000=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

Whakareatia te 370 ki te 1000000, ka 370000000.

$$370000000=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

Whakareatia te 286 ki te 400, ka 114400.

$$370000000=114400\left(950-\frac{x^{2}}{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 114400 ki te 950-\frac{x^{2}}{2}.

$$370000000=108680000+114400\left(-\frac{x^{2}}{2}\right)$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 114400 me te 2.

$$370000000=108680000-57200x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$108680000-57200x^{2}=370000000$$

Tangohia te 108680000 mai i ngā taha e rua.

$$-57200x^{2}=370000000-108680000$$

Tangohia te 108680000 i te 370000000, ka 261320000.

$$-57200x^{2}=261320000$$

Whakawehea ngā taha e rua ki te -57200.

$$x^{2}=\frac{261320000}{-57200}$$

Whakahekea te hautanga \frac{261320000}{-57200} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 400.

$$x^{2}=-\frac{653300}{143}$$

Kua oti te whārite te whakatau.

$$x=\frac{10\sqrt{934219}i}{143} x=-\frac{10\sqrt{934219}i}{143}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$370\times 10^{6}=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

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

$$370\times 1000000=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

Whakareatia te 370 ki te 1000000, ka 370000000.

$$370000000=286\times 400\left(950-\frac{x^{2}}{2}\right)$$

Whakareatia te 286 ki te 400, ka 114400.

$$370000000=114400\left(950-\frac{x^{2}}{2}\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 114400 ki te 950-\frac{x^{2}}{2}.

$$370000000=108680000+114400\left(-\frac{x^{2}}{2}\right)$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 114400 me te 2.

$$370000000=108680000-57200x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$108680000-57200x^{2}=370000000$$

Tangohia te 370000000 mai i ngā taha e rua.

$$108680000-57200x^{2}-370000000=0$$

Tangohia te 370000000 i te 108680000, ka -261320000.

$$-261320000-57200x^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$-57200x^{2}-261320000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -57200 mō a, 0 mō b, me -261320000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-57200\right)\left(-261320000\right)}}{2\left(-57200\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-57200\right)\left(-261320000\right)}}{2\left(-57200\right)}$$

Whakareatia -4 ki te -57200.

$$x=\frac{0±\sqrt{228800\left(-261320000\right)}}{2\left(-57200\right)}$$

Whakareatia 228800 ki te -261320000.

$$x=\frac{0±\sqrt{-59790016000000}}{2\left(-57200\right)}$$

Tuhia te pūtakerua o te -59790016000000.

$$x=\frac{0±8000\sqrt{934219}i}{2\left(-57200\right)}$$

Whakareatia 2 ki te -57200.

$$x=\frac{0±8000\sqrt{934219}i}{-114400}$$

Nā, me whakaoti te whārite x=\frac{0±8000\sqrt{934219}i}{-114400} ina he tāpiri te ±.

$$x=-\frac{10\sqrt{934219}i}{143}$$

Nā, me whakaoti te whārite x=\frac{0±8000\sqrt{934219}i}{-114400} ina he tango te ±.

$$x=\frac{10\sqrt{934219}i}{143}$$

Kua oti te whārite te whakatau.

$$x=-\frac{10\sqrt{934219}i}{143} x=\frac{10\sqrt{934219}i}{143}$$