Whakaoti i te 12!x+25x^2=26

$$12 ! x+25 { x }^{ 2 } =26$$

Whakaoti mō x

$$x=\frac{\sqrt{2294425328025626}}{5}-9580032\approx 0.000000054$$

$$x=-\frac{\sqrt{2294425328025626}}{5}-9580032\approx -19160064.000000052$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko te huarea o 12 ko 479001600.

$$479001600x+25x^{2}=26$$

Tangohia te 26 mai i ngā taha e rua.

$$479001600x+25x^{2}-26=0$$

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.

$$25x^{2}[phone]x-26=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 25 mō a, 479001600 mō b, me -26 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-479001600±\sqrt{479001600^{2}-4\times 25\left(-26\right)}}{2\times 25}$$

Pūrua 479001600.

$$x=\frac{-479001600±\sqrt{229442532802560000-4\times 25\left(-26\right)}}{2\times 25}$$

Whakareatia -4 ki te 25.

$$x=\frac{-479001600±\sqrt{229442532802560000-100\left(-26\right)}}{2\times 25}$$

Whakareatia -100 ki te -26.

$$x=\frac{-479001600±\sqrt{229442532802560000+2600}}{2\times 25}$$

Tāpiri 229442532802560000 ki te 2600.

$$x=\frac{-479001600±\sqrt{229442532802562600}}{2\times 25}$$

Tuhia te pūtakerua o te 229442532802562600.

$$x=\frac{-479001600±10\sqrt{2294425328025626}}{2\times 25}$$

Whakareatia 2 ki te 25.

$$x=\frac{-479001600±10\sqrt{2294425328025626}}{50}$$

Nā, me whakaoti te whārite x=\frac{-479001600±10\sqrt{2294425328025626}}{50} ina he tāpiri te ±. Tāpiri -479001600 ki te 10\sqrt{2294425328025626}.

$$x=\frac{10\sqrt{2294425328025626}-479001600}{50}$$

Whakawehe -479001600+10\sqrt{2294425328025626} ki te 50.

$$x=\frac{\sqrt{2294425328025626}}{5}-9580032$$

Nā, me whakaoti te whārite x=\frac{-479001600±10\sqrt{2294425328025626}}{50} ina he tango te ±. Tango 10\sqrt{2294425328025626} mai i -479001600.

$$x=\frac{-10\sqrt{2294425328025626}-479001600}{50}$$

Whakawehe -479001600-10\sqrt{2294425328025626} ki te 50.

$$x=-\frac{\sqrt{2294425328025626}}{5}-9580032$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{2294425328025626}}{5}-9580032 x=-\frac{\sqrt{2294425328025626}}{5}-9580032$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko te huarea o 12 ko 479001600.

$$479001600x+25x^{2}=26$$

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.

$$25x^{2}[phone]x=26$$

Whakawehea ngā taha e rua ki te 25.

$$\frac{25x^{2}[phone]x}{25}=\frac{26}{25}$$

Mā te whakawehe ki te 25 ka wetekia te whakareanga ki te 25.

$$x^{2}+\frac{479001600}{25}x=\frac{26}{25}$$

Whakawehe 479001600 ki te 25.

$$x^{2}[phone]x=\frac{26}{25}$$

Whakawehea te 19160064, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 9580032. Nā, tāpiria te pūrua o te 9580032 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}[phone]x+9580032^{2}=\frac{26}{25}+9580032^{2}$$

Pūrua 9580032.

$$x^{2}[phone]x+91777013121024=\frac{26}{25}[phone]$$

Tāpiri \frac{26}{25} ki te 91777013121024.

$$x^{2}[phone]x+91777013121024=\frac{2294425328025626}{25}$$

Tauwehea x^{2}[phone]x+91777013121024. 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}.

$$\left(x+9580032\right)^{2}=\frac{2294425328025626}{25}$$

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

$$\sqrt{\left(x+9580032\right)^{2}}=\sqrt{\frac{2294425328025626}{25}}$$

Whakarūnātia.

$$x+9580032=\frac{\sqrt{2294425328025626}}{5} x+9580032=-\frac{\sqrt{2294425328025626}}{5}$$

Me tango 9580032 mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{2294425328025626}}{5}-9580032 x=-\frac{\sqrt{2294425328025626}}{5}-9580032$$