Whakaoti i te x^2+1738x-20772=0

$${ x }^{ 2 } +1738x-20772=0$$

Whakaoti mō x (complex solution)

$$x=\sqrt{775933}-869\approx 11.870592085$$

$$x=-\left(\sqrt{775933}+869\right)\approx -1749.870592085$$

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.

$$x^{2}+1738x-20772=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 1738 mō b, me -20772 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1738±\sqrt{1738^{2}-4\left(-20772\right)}}{2}$$

Pūrua 1738.

$$x=\frac{-1738±\sqrt{3020644-4\left(-20772\right)}}{2}$$

Whakareatia -4 ki te -20772.

$$x=\frac{-1738±\sqrt{3020644+83088}}{2}$$

Tāpiri 3020644 ki te 83088.

$$x=\frac{-1738±\sqrt{3103732}}{2}$$

Tuhia te pūtakerua o te 3103732.

$$x=\frac{-1738±2\sqrt{775933}}{2}$$

Nā, me whakaoti te whārite x=\frac{-1738±2\sqrt{775933}}{2} ina he tāpiri te ±. Tāpiri -1738 ki te 2\sqrt{775933}.

$$x=\frac{2\sqrt{775933}-1738}{2}$$

Whakawehe -1738+2\sqrt{775933} ki te 2.

$$x=\sqrt{775933}-869$$

Nā, me whakaoti te whārite x=\frac{-1738±2\sqrt{775933}}{2} ina he tango te ±. Tango 2\sqrt{775933} mai i -1738.

$$x=\frac{-2\sqrt{775933}-1738}{2}$$

Whakawehe -1738-2\sqrt{775933} ki te 2.

$$x=-\sqrt{775933}-869$$

Kua oti te whārite te whakatau.

$$x=\sqrt{775933}-869 x=-\sqrt{775933}-869$$

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.

$$x^{2}+1738x-20772=0$$

Me tāpiri 20772 ki ngā taha e rua o te whārite.

$$x^{2}+1738x-20772-\left(-20772\right)=-\left(-20772\right)$$

Mā te tango i te -20772 i a ia ake anō ka toe ko te 0.

$$x^{2}+1738x=-\left(-20772\right)$$

Tango -20772 mai i 0.

$$x^{2}+1738x=20772$$

Whakawehea te 1738, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 869. Nā, tāpiria te pūrua o te 869 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+1738x+869^{2}=20772+869^{2}$$

Pūrua 869.

$$x^{2}+1738x+755161=20772+755161$$

Tāpiri 20772 ki te 755161.

$$x^{2}+1738x+755161=775933$$

Tauwehea x^{2}+1738x+755161. 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}.

$$\left(x+869\right)^{2}=775933$$

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

$$\sqrt{\left(x+869\right)^{2}}=\sqrt{775933}$$

Whakarūnātia.

$$x+869=\sqrt{775933} x+869=-\sqrt{775933}$$

Me tango 869 mai i ngā taha e rua o te whārite.

$$x=\sqrt{775933}-869 x=-\sqrt{775933}-869$$

Whakaoti mō x

$$x=\sqrt{775933}-869\approx 11.870592085$$

$$x=-\sqrt{775933}-869\approx -1749.870592085$$

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.

$$x^{2}+1738x-20772=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 1738 mō b, me -20772 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1738±\sqrt{1738^{2}-4\left(-20772\right)}}{2}$$

Pūrua 1738.

$$x=\frac{-1738±\sqrt{3020644-4\left(-20772\right)}}{2}$$

Whakareatia -4 ki te -20772.

$$x=\frac{-1738±\sqrt{3020644+83088}}{2}$$

Tāpiri 3020644 ki te 83088.

$$x=\frac{-1738±\sqrt{3103732}}{2}$$

Tuhia te pūtakerua o te 3103732.

$$x=\frac{-1738±2\sqrt{775933}}{2}$$

Nā, me whakaoti te whārite x=\frac{-1738±2\sqrt{775933}}{2} ina he tāpiri te ±. Tāpiri -1738 ki te 2\sqrt{775933}.

$$x=\frac{2\sqrt{775933}-1738}{2}$$

Whakawehe -1738+2\sqrt{775933} ki te 2.

$$x=\sqrt{775933}-869$$

Nā, me whakaoti te whārite x=\frac{-1738±2\sqrt{775933}}{2} ina he tango te ±. Tango 2\sqrt{775933} mai i -1738.

$$x=\frac{-2\sqrt{775933}-1738}{2}$$

Whakawehe -1738-2\sqrt{775933} ki te 2.

$$x=-\sqrt{775933}-869$$

Kua oti te whārite te whakatau.

$$x=\sqrt{775933}-869 x=-\sqrt{775933}-869$$

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.

$$x^{2}+1738x-20772=0$$

Me tāpiri 20772 ki ngā taha e rua o te whārite.

$$x^{2}+1738x-20772-\left(-20772\right)=-\left(-20772\right)$$

Mā te tango i te -20772 i a ia ake anō ka toe ko te 0.

$$x^{2}+1738x=-\left(-20772\right)$$

Tango -20772 mai i 0.

$$x^{2}+1738x=20772$$

Whakawehea te 1738, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 869. Nā, tāpiria te pūrua o te 869 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+1738x+869^{2}=20772+869^{2}$$

Pūrua 869.

$$x^{2}+1738x+755161=20772+755161$$

Tāpiri 20772 ki te 755161.

$$x^{2}+1738x+755161=775933$$

Tauwehea x^{2}+1738x+755161. 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}.

$$\left(x+869\right)^{2}=775933$$

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

$$\sqrt{\left(x+869\right)^{2}}=\sqrt{775933}$$

Whakarūnātia.

$$x+869=\sqrt{775933} x+869=-\sqrt{775933}$$

Me tango 869 mai i ngā taha e rua o te whārite.

$$x=\sqrt{775933}-869 x=-\sqrt{775933}-869$$