Whakaoti i te x=425x^2+635x-39075

$$x=425 { x }^{ 2 } +635x-39075$$

Whakaoti mō x

$$x = \frac{2 \sqrt{4176841} - 317}{425} \approx 8.87168059$$

$$x=\frac{-2\sqrt{4176841}-317}{425}\approx -10.363445296$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 425x^{2} mai i ngā taha e rua.

$$x-425x^{2}=635x-39075$$

Tangohia te 635x mai i ngā taha e rua.

$$x-425x^{2}-635x=-39075$$

Pahekotia te x me -635x, ka -634x.

$$-634x-425x^{2}=-39075$$

Me tāpiri te 39075 ki ngā taha e rua.

$$-634x-425x^{2}+39075=0$$

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.

$$-425x^{2}-634x+39075=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -425 mō a, -634 mō b, me 39075 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-634\right)±\sqrt{\left(-634\right)^{2}-4\left(-425\right)\times 39075}}{2\left(-425\right)}$$

Pūrua -634.

$$x=\frac{-\left(-634\right)±\sqrt{401956-4\left(-425\right)\times 39075}}{2\left(-425\right)}$$

Whakareatia -4 ki te -425.

$$x=\frac{-\left(-634\right)±\sqrt{401956+1700\times 39075}}{2\left(-425\right)}$$

Whakareatia 1700 ki te 39075.

$$x=\frac{-\left(-634\right)±\sqrt{401956+66427500}}{2\left(-425\right)}$$

Tāpiri 401956 ki te 66427500.

$$x=\frac{-\left(-634\right)±\sqrt{66829456}}{2\left(-425\right)}$$

Tuhia te pūtakerua o te 66829456.

$$x=\frac{-\left(-634\right)±4\sqrt{4176841}}{2\left(-425\right)}$$

Ko te tauaro o -634 ko 634.

$$x=\frac{634±4\sqrt{4176841}}{2\left(-425\right)}$$

Whakareatia 2 ki te -425.

$$x=\frac{634±4\sqrt{4176841}}{-850}$$

Nā, me whakaoti te whārite x=\frac{634±4\sqrt{4176841}}{-850} ina he tāpiri te ±. Tāpiri 634 ki te 4\sqrt{4176841}.

$$x=\frac{4\sqrt{4176841}+634}{-850}$$

Whakawehe 634+4\sqrt{4176841} ki te -850.

$$x=\frac{-2\sqrt{4176841}-317}{425}$$

Nā, me whakaoti te whārite x=\frac{634±4\sqrt{4176841}}{-850} ina he tango te ±. Tango 4\sqrt{4176841} mai i 634.

$$x=\frac{634-4\sqrt{4176841}}{-850}$$

Whakawehe 634-4\sqrt{4176841} ki te -850.

$$x=\frac{2\sqrt{4176841}-317}{425}$$

Kua oti te whārite te whakatau.

$$x=\frac{-2\sqrt{4176841}-317}{425} x=\frac{2\sqrt{4176841}-317}{425}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 425x^{2} mai i ngā taha e rua.

$$x-425x^{2}=635x-39075$$

Tangohia te 635x mai i ngā taha e rua.

$$x-425x^{2}-635x=-39075$$

Pahekotia te x me -635x, ka -634x.

$$-634x-425x^{2}=-39075$$

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.

$$-425x^{2}-634x=-39075$$

Whakawehea ngā taha e rua ki te -425.

$$\frac{-425x^{2}-634x}{-425}=-\frac{39075}{-425}$$

Mā te whakawehe ki te -425 ka wetekia te whakareanga ki te -425.

$$x^{2}+\left(-\frac{634}{-425}\right)x=-\frac{39075}{-425}$$

Whakawehe -634 ki te -425.

$$x^{2}+\frac{634}{425}x=-\frac{39075}{-425}$$

Whakahekea te hautanga \frac{-39075}{-425} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$x^{2}+\frac{634}{425}x=\frac{1563}{17}$$

Whakawehea te \frac{634}{425}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{317}{425}. Nā, tāpiria te pūrua o te \frac{317}{425} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{634}{425}x+\left(\frac{317}{425}\right)^{2}=\frac{1563}{17}+\left(\frac{317}{425}\right)^{2}$$

Pūruatia \frac{317}{425} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{634}{425}x+\frac{100489}{180625}=\frac{1563}{17}+\frac{100489}{180625}$$

Tāpiri \frac{1563}{17} ki te \frac{100489}{180625} 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.

$$x^{2}+\frac{634}{425}x+\frac{100489}{180625}=\frac{16707364}{180625}$$

Tauwehea x^{2}+\frac{634}{425}x+\frac{100489}{180625}. 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}.

$$\left(x+\frac{317}{425}\right)^{2}=\frac{16707364}{180625}$$

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

$$\sqrt{\left(x+\frac{317}{425}\right)^{2}}=\sqrt{\frac{16707364}{180625}}$$

Whakarūnātia.

$$x+\frac{317}{425}=\frac{2\sqrt{4176841}}{425} x+\frac{317}{425}=-\frac{2\sqrt{4176841}}{425}$$

Me tango \frac{317}{425} mai i ngā taha e rua o te whārite.

$$x=\frac{2\sqrt{4176841}-317}{425} x=\frac{-2\sqrt{4176841}-317}{425}$$