Whakaoti i te x=4.25x^2+635x-39075

$$x=4.25 { x }^{ 2 } +635x-39075$$

Whakaoti mō x

$$x = \frac{2 \sqrt{1066231} - 1268}{17} \approx 46.89230838$$

$$x=\frac{-2\sqrt{1066231}-1268}{17}\approx -196.068778968$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 4.25x^{2} mai i ngā taha e rua.

$$x-4.25x^{2}=635x-39075$$

Tangohia te 635x mai i ngā taha e rua.

$$x-4.25x^{2}-635x=-39075$$

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

$$-634x-4.25x^{2}=-39075$$

Me tāpiri te 39075 ki ngā taha e rua.

$$-634x-4.25x^{2}+39075=0$$

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.

$$-4.25x^{2}-634x+39075=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -4.25 mō a, -634 mō b, me 39075 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-634\right)±\sqrt{\left(-634\right)^{2}-4\left(-4.25\right)\times 39075}}{2\left(-4.25\right)}$$

Pūrua -634.

$$x=\frac{-\left(-634\right)±\sqrt{401956-4\left(-4.25\right)\times 39075}}{2\left(-4.25\right)}$$

Whakareatia -4 ki te -4.25.

$$x=\frac{-\left(-634\right)±\sqrt{401956+17\times 39075}}{2\left(-4.25\right)}$$

Whakareatia 17 ki te 39075.

$$x=\frac{-\left(-634\right)±\sqrt{401956+664275}}{2\left(-4.25\right)}$$

Tāpiri 401956 ki te 664275.

$$x=\frac{-\left(-634\right)±\sqrt{1066231}}{2\left(-4.25\right)}$$

Ko te tauaro o -634 ko 634.

$$x=\frac{634±\sqrt{1066231}}{2\left(-4.25\right)}$$

Whakareatia 2 ki te -4.25.

$$x=\frac{634±\sqrt{1066231}}{-8.5}$$

Nā, me whakaoti te whārite x=\frac{634±\sqrt{1066231}}{-8.5} ina he tāpiri te ±. Tāpiri 634 ki te \sqrt{1066231}.

$$x=\frac{\sqrt{1066231}+634}{-8.5}$$

Whakawehe 634+\sqrt{1066231} ki te -8.5 mā te whakarea 634+\sqrt{1066231} ki te tau huripoki o -8.5.

$$x=\frac{-2\sqrt{1066231}-1268}{17}$$

Nā, me whakaoti te whārite x=\frac{634±\sqrt{1066231}}{-8.5} ina he tango te ±. Tango \sqrt{1066231} mai i 634.

$$x=\frac{634-\sqrt{1066231}}{-8.5}$$

Whakawehe 634-\sqrt{1066231} ki te -8.5 mā te whakarea 634-\sqrt{1066231} ki te tau huripoki o -8.5.

$$x=\frac{2\sqrt{1066231}-1268}{17}$$

Kua oti te whārite te whakatau.

$$x=\frac{-2\sqrt{1066231}-1268}{17} x=\frac{2\sqrt{1066231}-1268}{17}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 4.25x^{2} mai i ngā taha e rua.

$$x-4.25x^{2}=635x-39075$$

Tangohia te 635x mai i ngā taha e rua.

$$x-4.25x^{2}-635x=-39075$$

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

$$-634x-4.25x^{2}=-39075$$

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.

$$-4.25x^{2}-634x=-39075$$

Whakawehea ngā taha e rua o te whārite ki te -4.25, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{-4.25x^{2}-634x}{-4.25}=-\frac{39075}{-4.25}$$

Mā te whakawehe ki te -4.25 ka wetekia te whakareanga ki te -4.25.

$$x^{2}+\left(-\frac{634}{-4.25}\right)x=-\frac{39075}{-4.25}$$

Whakawehe -634 ki te -4.25 mā te whakarea -634 ki te tau huripoki o -4.25.

$$x^{2}+\frac{2536}{17}x=-\frac{39075}{-4.25}$$

Whakawehe -39075 ki te -4.25 mā te whakarea -39075 ki te tau huripoki o -4.25.

$$x^{2}+\frac{2536}{17}x=\frac{156300}{17}$$

Whakawehea te \frac{2536}{17}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1268}{17}. Nā, tāpiria te pūrua o te \frac{1268}{17} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{2536}{17}x+\frac{1268}{17}^{2}=\frac{156300}{17}+\frac{1268}{17}^{2}$$

Pūruatia \frac{1268}{17} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{2536}{17}x+\frac{1607824}{289}=\frac{156300}{17}+\frac{1607824}{289}$$

Tāpiri \frac{156300}{17} ki te \frac{1607824}{289} 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.

$$x^{2}+\frac{2536}{17}x+\frac{1607824}{289}=\frac{4264924}{289}$$

Tauwehea x^{2}+\frac{2536}{17}x+\frac{1607824}{289}. 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}.

$$\left(x+\frac{1268}{17}\right)^{2}=\frac{4264924}{289}$$

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

$$\sqrt{\left(x+\frac{1268}{17}\right)^{2}}=\sqrt{\frac{4264924}{289}}$$

Whakarūnātia.

$$x+\frac{1268}{17}=\frac{2\sqrt{1066231}}{17} x+\frac{1268}{17}=-\frac{2\sqrt{1066231}}{17}$$

Me tango \frac{1268}{17} mai i ngā taha e rua o te whārite.

$$x=\frac{2\sqrt{1066231}-1268}{17} x=\frac{-2\sqrt{1066231}-1268}{17}$$