Whakaoti i te x^2+16x-10=0

$$x ^ { 2 } + 16 x - 10 = 0$$

Whakaoti mō x (complex solution)

$$x=\sqrt{74}-8\approx 0.602325267$$

$$x=-\left(\sqrt{74}+8\right)\approx -16.602325267$$

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.

$$x^{2}+16x-10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 16 mō b, me -10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-10\right)}}{2}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\left(-10\right)}}{2}$$

Whakareatia -4 ki te -10.

$$x=\frac{-16±\sqrt{256+40}}{2}$$

Tāpiri 256 ki te 40.

$$x=\frac{-16±\sqrt{296}}{2}$$

Tuhia te pūtakerua o te 296.

$$x=\frac{-16±2\sqrt{74}}{2}$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{74}}{2} ina he tāpiri te ±. Tāpiri -16 ki te 2\sqrt{74}.

$$x=\frac{2\sqrt{74}-16}{2}$$

Whakawehe -16+2\sqrt{74} ki te 2.

$$x=\sqrt{74}-8$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{74}}{2} ina he tango te ±. Tango 2\sqrt{74} mai i -16.

$$x=\frac{-2\sqrt{74}-16}{2}$$

Whakawehe -16-2\sqrt{74} ki te 2.

$$x=-\sqrt{74}-8$$

Kua oti te whārite te whakatau.

$$x=\sqrt{74}-8 x=-\sqrt{74}-8$$

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.

$$x^{2}+16x-10=0$$

Me tāpiri 10 ki ngā taha e rua o te whārite.

$$x^{2}+16x-10-\left(-10\right)=-\left(-10\right)$$

Mā te tango i te -10 i a ia ake anō ka toe ko te 0.

$$x^{2}+16x=-\left(-10\right)$$

Tango -10 mai i 0.

$$x^{2}+16x=10$$

Whakawehea te 16, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 8. Nā, tāpiria te pūrua o te 8 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+16x+8^{2}=10+8^{2}$$

Pūrua 8.

$$x^{2}+16x+64=10+64$$

Tāpiri 10 ki te 64.

$$x^{2}+16x+64=74$$

Tauwehea x^{2}+16x+64. 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}.

$$\left(x+8\right)^{2}=74$$

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

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{74}$$

Whakarūnātia.

$$x+8=\sqrt{74} x+8=-\sqrt{74}$$

Me tango 8 mai i ngā taha e rua o te whārite.

$$x=\sqrt{74}-8 x=-\sqrt{74}-8$$

Whakaoti mō x

$$x=\sqrt{74}-8\approx 0.602325267$$

$$x=-\sqrt{74}-8\approx -16.602325267$$

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.

$$x^{2}+16x-10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 16 mō b, me -10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-10\right)}}{2}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\left(-10\right)}}{2}$$

Whakareatia -4 ki te -10.

$$x=\frac{-16±\sqrt{256+40}}{2}$$

Tāpiri 256 ki te 40.

$$x=\frac{-16±\sqrt{296}}{2}$$

Tuhia te pūtakerua o te 296.

$$x=\frac{-16±2\sqrt{74}}{2}$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{74}}{2} ina he tāpiri te ±. Tāpiri -16 ki te 2\sqrt{74}.

$$x=\frac{2\sqrt{74}-16}{2}$$

Whakawehe -16+2\sqrt{74} ki te 2.

$$x=\sqrt{74}-8$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{74}}{2} ina he tango te ±. Tango 2\sqrt{74} mai i -16.

$$x=\frac{-2\sqrt{74}-16}{2}$$

Whakawehe -16-2\sqrt{74} ki te 2.

$$x=-\sqrt{74}-8$$

Kua oti te whārite te whakatau.

$$x=\sqrt{74}-8 x=-\sqrt{74}-8$$

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.

$$x^{2}+16x-10=0$$

Me tāpiri 10 ki ngā taha e rua o te whārite.

$$x^{2}+16x-10-\left(-10\right)=-\left(-10\right)$$

Mā te tango i te -10 i a ia ake anō ka toe ko te 0.

$$x^{2}+16x=-\left(-10\right)$$

Tango -10 mai i 0.

$$x^{2}+16x=10$$

Whakawehea te 16, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 8. Nā, tāpiria te pūrua o te 8 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+16x+8^{2}=10+8^{2}$$

Pūrua 8.

$$x^{2}+16x+64=10+64$$

Tāpiri 10 ki te 64.

$$x^{2}+16x+64=74$$

Tauwehea x^{2}+16x+64. 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}.

$$\left(x+8\right)^{2}=74$$

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

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{74}$$

Whakarūnātia.

$$x+8=\sqrt{74} x+8=-\sqrt{74}$$

Me tango 8 mai i ngā taha e rua o te whārite.

$$x=\sqrt{74}-8 x=-\sqrt{74}-8$$