Whakaoti i te 4x+55x-9^2=99999x^2

$$4x+55x- { 9 }^{ 2 } =99999 { x }^{ 2 }$$

Whakaoti mō x (complex solution)

$$x=\frac{-\sqrt{32396195}i+59}{199998}\approx 0.000295003-0.028459112i$$

$$x=\frac{59+\sqrt{32396195}i}{199998}\approx 0.000295003+0.028459112i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 4x me 55x, ka 59x.

$$59x-9^{2}=99999x^{2}$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$59x-81=99999x^{2}$$

Tangohia te 99999x^{2} mai i ngā taha e rua.

$$59x-81-99999x^{2}=0$$

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.

$$-99999x^{2}+59x-81=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -99999 mō a, 59 mō b, me -81 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-59±\sqrt{59^{2}-4\left(-99999\right)\left(-81\right)}}{2\left(-99999\right)}$$

Pūrua 59.

$$x=\frac{-59±\sqrt{3481-4\left(-99999\right)\left(-81\right)}}{2\left(-99999\right)}$$

Whakareatia -4 ki te -99999.

$$x=\frac{-59±\sqrt{3481+399996\left(-81\right)}}{2\left(-99999\right)}$$

Whakareatia 399996 ki te -81.

$$x=\frac{-59±\sqrt{3481-32399676}}{2\left(-99999\right)}$$

Tāpiri 3481 ki te -32399676.

$$x=\frac{-59±\sqrt{-32396195}}{2\left(-99999\right)}$$

Tuhia te pūtakerua o te -32396195.

$$x=\frac{-59±\sqrt{32396195}i}{2\left(-99999\right)}$$

Whakareatia 2 ki te -99999.

$$x=\frac{-59±\sqrt{32396195}i}{-199998}$$

Nā, me whakaoti te whārite x=\frac{-59±\sqrt{32396195}i}{-199998} ina he tāpiri te ±. Tāpiri -59 ki te i\sqrt{32396195}.

$$x=\frac{-59+\sqrt{32396195}i}{-199998}$$

Whakawehe -59+i\sqrt{32396195} ki te -199998.

$$x=\frac{-\sqrt{32396195}i+59}{199998}$$

Nā, me whakaoti te whārite x=\frac{-59±\sqrt{32396195}i}{-199998} ina he tango te ±. Tango i\sqrt{32396195} mai i -59.

$$x=\frac{-\sqrt{32396195}i-59}{-199998}$$

Whakawehe -59-i\sqrt{32396195} ki te -199998.

$$x=\frac{59+\sqrt{32396195}i}{199998}$$

Kua oti te whārite te whakatau.

$$x=\frac{-\sqrt{32396195}i+59}{199998} x=\frac{59+\sqrt{32396195}i}{199998}$$

Ngā Upane mō te Whakaoti i te Pūrua

Pahekotia te 4x me 55x, ka 59x.

$$59x-9^{2}=99999x^{2}$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$59x-81=99999x^{2}$$

Tangohia te 99999x^{2} mai i ngā taha e rua.

$$59x-81-99999x^{2}=0$$

Me tāpiri te 81 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$59x-99999x^{2}=81$$

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.

$$-99999x^{2}+59x=81$$

Whakawehea ngā taha e rua ki te -99999.

$$\frac{-99999x^{2}+59x}{-99999}=\frac{81}{-99999}$$

Mā te whakawehe ki te -99999 ka wetekia te whakareanga ki te -99999.

$$x^{2}+\frac{59}{-99999}x=\frac{81}{-99999}$$

Whakawehe 59 ki te -99999.

$$x^{2}-\frac{59}{99999}x=\frac{81}{-99999}$$

Whakahekea te hautanga \frac{81}{-99999} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 9.

$$x^{2}-\frac{59}{99999}x=-\frac{9}{11111}$$

Whakawehea te -\frac{59}{99999}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{59}{199998}. Nā, tāpiria te pūrua o te -\frac{59}{199998} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{59}{99999}x+\left(-\frac{59}{199998}\right)^{2}=-\frac{9}{11111}+\left(-\frac{59}{199998}\right)^{2}$$

Pūruatia -\frac{59}{199998} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{59}{99999}x+\frac{3481}{39999200004}=-\frac{9}{11111}+\frac{3481}{39999200004}$$

Tāpiri -\frac{9}{11111} ki te \frac{3481}{39999200004} 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.

$$x^{2}-\frac{59}{99999}x+\frac{3481}{39999200004}=-\frac{32396195}{39999200004}$$

Tauwehea x^{2}-\frac{59}{99999}x+\frac{3481}{39999200004}. 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}.

$$\left(x-\frac{59}{199998}\right)^{2}=-\frac{32396195}{39999200004}$$

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

$$\sqrt{\left(x-\frac{59}{199998}\right)^{2}}=\sqrt{-\frac{32396195}{39999200004}}$$

Whakarūnātia.

$$x-\frac{59}{199998}=\frac{\sqrt{32396195}i}{199998} x-\frac{59}{199998}=-\frac{\sqrt{32396195}i}{199998}$$

Me tāpiri \frac{59}{199998} ki ngā taha e rua o te whārite.

$$x=\frac{59+\sqrt{32396195}i}{199998} x=\frac{-\sqrt{32396195}i+59}{199998}$$