Whakaoti i te x^2+52x-45=0

$${ x }^{ 2 } +52x-45=0$$

Whakaoti mō x (complex solution)

$$x=\sqrt{721}-26\approx 0.851443164$$

$$x=-\left(\sqrt{721}+26\right)\approx -52.851443164$$

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.

$$x^{2}+52x-45=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 52 mō b, me -45 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-52±\sqrt{52^{2}-4\left(-45\right)}}{2}$$

Pūrua 52.

$$x=\frac{-52±\sqrt{2704-4\left(-45\right)}}{2}$$

Whakareatia -4 ki te -45.

$$x=\frac{-52±\sqrt{2704+180}}{2}$$

Tāpiri 2704 ki te 180.

$$x=\frac{-52±\sqrt{2884}}{2}$$

Tuhia te pūtakerua o te 2884.

$$x=\frac{-52±2\sqrt{721}}{2}$$

Nā, me whakaoti te whārite x=\frac{-52±2\sqrt{721}}{2} ina he tāpiri te ±. Tāpiri -52 ki te 2\sqrt{721}.

$$x=\frac{2\sqrt{721}-52}{2}$$

Whakawehe -52+2\sqrt{721} ki te 2.

$$x=\sqrt{721}-26$$

Nā, me whakaoti te whārite x=\frac{-52±2\sqrt{721}}{2} ina he tango te ±. Tango 2\sqrt{721} mai i -52.

$$x=\frac{-2\sqrt{721}-52}{2}$$

Whakawehe -52-2\sqrt{721} ki te 2.

$$x=-\sqrt{721}-26$$

Kua oti te whārite te whakatau.

$$x=\sqrt{721}-26 x=-\sqrt{721}-26$$

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.

$$x^{2}+52x-45=0$$

Me tāpiri 45 ki ngā taha e rua o te whārite.

$$x^{2}+52x-45-\left(-45\right)=-\left(-45\right)$$

Mā te tango i te -45 i a ia ake anō ka toe ko te 0.

$$x^{2}+52x=-\left(-45\right)$$

Tango -45 mai i 0.

$$x^{2}+52x=45$$

Whakawehea te 52, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 26. Nā, tāpiria te pūrua o te 26 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+52x+26^{2}=45+26^{2}$$

Pūrua 26.

$$x^{2}+52x+676=45+676$$

Tāpiri 45 ki te 676.

$$x^{2}+52x+676=721$$

Tauwehea x^{2}+52x+676. 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}.

$$\left(x+26\right)^{2}=721$$

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

$$\sqrt{\left(x+26\right)^{2}}=\sqrt{721}$$

Whakarūnātia.

$$x+26=\sqrt{721} x+26=-\sqrt{721}$$

Me tango 26 mai i ngā taha e rua o te whārite.

$$x=\sqrt{721}-26 x=-\sqrt{721}-26$$

Whakaoti mō x

$$x=\sqrt{721}-26\approx 0.851443164$$

$$x=-\sqrt{721}-26\approx -52.851443164$$

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.

$$x^{2}+52x-45=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 52 mō b, me -45 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-52±\sqrt{52^{2}-4\left(-45\right)}}{2}$$

Pūrua 52.

$$x=\frac{-52±\sqrt{2704-4\left(-45\right)}}{2}$$

Whakareatia -4 ki te -45.

$$x=\frac{-52±\sqrt{2704+180}}{2}$$

Tāpiri 2704 ki te 180.

$$x=\frac{-52±\sqrt{2884}}{2}$$

Tuhia te pūtakerua o te 2884.

$$x=\frac{-52±2\sqrt{721}}{2}$$

Nā, me whakaoti te whārite x=\frac{-52±2\sqrt{721}}{2} ina he tāpiri te ±. Tāpiri -52 ki te 2\sqrt{721}.

$$x=\frac{2\sqrt{721}-52}{2}$$

Whakawehe -52+2\sqrt{721} ki te 2.

$$x=\sqrt{721}-26$$

Nā, me whakaoti te whārite x=\frac{-52±2\sqrt{721}}{2} ina he tango te ±. Tango 2\sqrt{721} mai i -52.

$$x=\frac{-2\sqrt{721}-52}{2}$$

Whakawehe -52-2\sqrt{721} ki te 2.

$$x=-\sqrt{721}-26$$

Kua oti te whārite te whakatau.

$$x=\sqrt{721}-26 x=-\sqrt{721}-26$$

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.

$$x^{2}+52x-45=0$$

Me tāpiri 45 ki ngā taha e rua o te whārite.

$$x^{2}+52x-45-\left(-45\right)=-\left(-45\right)$$

Mā te tango i te -45 i a ia ake anō ka toe ko te 0.

$$x^{2}+52x=-\left(-45\right)$$

Tango -45 mai i 0.

$$x^{2}+52x=45$$

Whakawehea te 52, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 26. Nā, tāpiria te pūrua o te 26 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+52x+26^{2}=45+26^{2}$$

Pūrua 26.

$$x^{2}+52x+676=45+676$$

Tāpiri 45 ki te 676.

$$x^{2}+52x+676=721$$

Tauwehea x^{2}+52x+676. 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}.

$$\left(x+26\right)^{2}=721$$

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

$$\sqrt{\left(x+26\right)^{2}}=\sqrt{721}$$

Whakarūnātia.

$$x+26=\sqrt{721} x+26=-\sqrt{721}$$

Me tango 26 mai i ngā taha e rua o te whārite.

$$x=\sqrt{721}-26 x=-\sqrt{721}-26$$