Whakaoti i te 29500x^2-7644x=40248

$$29500 x ^ { 2 } - 7644 x = 40248$$

Whakaoti mō x

$$x = \frac{9 \sqrt{3709641} + 1911}{14750} \approx 1.304771899$$

$$x=\frac{1911-9\sqrt{3709641}}{14750}\approx -1.045653255$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$29500x^{2}-7644x=40248$$

Me tango 40248 mai i ngā taha e rua o te whārite.

$$29500x^{2}-7644x-40248=40248-40248$$

Mā te tango i te 40248 i a ia ake anō ka toe ko te 0.

$$29500x^{2}-7644x-40248=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 29500 mō a, -7644 mō b, me -40248 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7644\right)±\sqrt{\left(-7644\right)^{2}-4\times 29500\left(-40248\right)}}{2\times 29500}$$

Pūrua -7644.

$$x=\frac{-\left(-7644\right)±\sqrt{58430736-4\times 29500\left(-40248\right)}}{2\times 29500}$$

Whakareatia -4 ki te 29500.

$$x=\frac{-\left(-7644\right)±\sqrt{58430736-118000\left(-40248\right)}}{2\times 29500}$$

Whakareatia -118000 ki te -40248.

$$x=\frac{-\left(-7644\right)±\sqrt{58430736+4749264000}}{2\times 29500}$$

Tāpiri 58430736 ki te 4749264000.

$$x=\frac{-\left(-7644\right)±\sqrt{4807694736}}{2\times 29500}$$

Tuhia te pūtakerua o te 4807694736.

$$x=\frac{-\left(-7644\right)±36\sqrt{3709641}}{2\times 29500}$$

Ko te tauaro o -7644 ko 7644.

$$x=\frac{7644±36\sqrt{3709641}}{2\times 29500}$$

Whakareatia 2 ki te 29500.

$$x=\frac{7644±36\sqrt{3709641}}{59000}$$

Nā, me whakaoti te whārite x=\frac{7644±36\sqrt{3709641}}{59000} ina he tāpiri te ±. Tāpiri 7644 ki te 36\sqrt{3709641}.

$$x=\frac{36\sqrt{3709641}+7644}{59000}$$

Whakawehe 7644+36\sqrt{3709641} ki te 59000.

$$x=\frac{9\sqrt{3709641}+1911}{14750}$$

Nā, me whakaoti te whārite x=\frac{7644±36\sqrt{3709641}}{59000} ina he tango te ±. Tango 36\sqrt{3709641} mai i 7644.

$$x=\frac{7644-36\sqrt{3709641}}{59000}$$

Whakawehe 7644-36\sqrt{3709641} ki te 59000.

$$x=\frac{1911-9\sqrt{3709641}}{14750}$$

Kua oti te whārite te whakatau.

$$x=\frac{9\sqrt{3709641}+1911}{14750} x=\frac{1911-9\sqrt{3709641}}{14750}$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$29500x^{2}-7644x=40248$$

Whakawehea ngā taha e rua ki te 29500.

$$\frac{29500x^{2}-7644x}{29500}=\frac{40248}{29500}$$

Mā te whakawehe ki te 29500 ka wetekia te whakareanga ki te 29500.

$$x^{2}+\left(-\frac{7644}{29500}\right)x=\frac{40248}{29500}$$

Whakahekea te hautanga \frac{-7644}{29500} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{1911}{7375}x=\frac{40248}{29500}$$

Whakahekea te hautanga \frac{40248}{29500} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{1911}{7375}x=\frac{10062}{7375}$$

Whakawehea te -\frac{1911}{7375}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1911}{14750}. Nā, tāpiria te pūrua o te -\frac{1911}{14750} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1911}{7375}x+\left(-\frac{1911}{14750}\right)^{2}=\frac{10062}{7375}+\left(-\frac{1911}{14750}\right)^{2}$$

Pūruatia -\frac{1911}{14750} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1911}{7375}x+\frac{3651921}{217562500}=\frac{10062}{7375}+\frac{3651921}{217562500}$$

Tāpiri \frac{10062}{7375} ki te \frac{3651921}{217562500} 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.

$$x^{2}-\frac{1911}{7375}x+\frac{3651921}{217562500}=\frac{300480921}{217562500}$$

Tauwehea x^{2}-\frac{1911}{7375}x+\frac{3651921}{217562500}. 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}.

$$\left(x-\frac{1911}{14750}\right)^{2}=\frac{300480921}{217562500}$$

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

$$\sqrt{\left(x-\frac{1911}{14750}\right)^{2}}=\sqrt{\frac{300480921}{217562500}}$$

Whakarūnātia.

$$x-\frac{1911}{14750}=\frac{9\sqrt{3709641}}{14750} x-\frac{1911}{14750}=-\frac{9\sqrt{3709641}}{14750}$$

Me tāpiri \frac{1911}{14750} ki ngā taha e rua o te whārite.

$$x=\frac{9\sqrt{3709641}+1911}{14750} x=\frac{1911-9\sqrt{3709641}}{14750}$$