Whakaoti i te 8x=1-x^2

$$8 x = 1 - x ^ { 2 }$$

Whakaoti mō x (complex solution)

$$x=\sqrt{17}-4\approx 0.123105626$$

$$x=-\left(\sqrt{17}+4\right)\approx -8.123105626$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 1 mai i ngā taha e rua.

$$8x-1=-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$8x-1+x^{2}=0$$

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.

$$x^{2}+8x-1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 8 mō b, me -1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-1\right)}}{2}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\left(-1\right)}}{2}$$

Whakareatia -4 ki te -1.

$$x=\frac{-8±\sqrt{64+4}}{2}$$

Tāpiri 64 ki te 4.

$$x=\frac{-8±\sqrt{68}}{2}$$

Tuhia te pūtakerua o te 68.

$$x=\frac{-8±2\sqrt{17}}{2}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{17}}{2} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{17}.

$$x=\frac{2\sqrt{17}-8}{2}$$

Whakawehe -8+2\sqrt{17} ki te 2.

$$x=\sqrt{17}-4$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{17}}{2} ina he tango te ±. Tango 2\sqrt{17} mai i -8.

$$x=\frac{-2\sqrt{17}-8}{2}$$

Whakawehe -8-2\sqrt{17} ki te 2.

$$x=-\sqrt{17}-4$$

Kua oti te whārite te whakatau.

$$x=\sqrt{17}-4 x=-\sqrt{17}-4$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te x^{2} ki ngā taha e rua.

$$8x+x^{2}=1$$

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.

$$x^{2}+8x=1$$

Whakawehea te 8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 4. Nā, tāpiria te pūrua o te 4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+8x+4^{2}=1+4^{2}$$

Pūrua 4.

$$x^{2}+8x+16=1+16$$

Tāpiri 1 ki te 16.

$$x^{2}+8x+16=17$$

Tauwehea x^{2}+8x+16. 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}.

$$\left(x+4\right)^{2}=17$$

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

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{17}$$

Whakarūnātia.

$$x+4=\sqrt{17} x+4=-\sqrt{17}$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$x=\sqrt{17}-4 x=-\sqrt{17}-4$$

Whakaoti mō x

$$x=\sqrt{17}-4\approx 0.123105626$$

$$x=-\sqrt{17}-4\approx -8.123105626$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 1 mai i ngā taha e rua.

$$8x-1=-x^{2}$$

Me tāpiri te x^{2} ki ngā taha e rua.

$$8x-1+x^{2}=0$$

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.

$$x^{2}+8x-1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 8 mō b, me -1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-1\right)}}{2}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\left(-1\right)}}{2}$$

Whakareatia -4 ki te -1.

$$x=\frac{-8±\sqrt{64+4}}{2}$$

Tāpiri 64 ki te 4.

$$x=\frac{-8±\sqrt{68}}{2}$$

Tuhia te pūtakerua o te 68.

$$x=\frac{-8±2\sqrt{17}}{2}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{17}}{2} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{17}.

$$x=\frac{2\sqrt{17}-8}{2}$$

Whakawehe -8+2\sqrt{17} ki te 2.

$$x=\sqrt{17}-4$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{17}}{2} ina he tango te ±. Tango 2\sqrt{17} mai i -8.

$$x=\frac{-2\sqrt{17}-8}{2}$$

Whakawehe -8-2\sqrt{17} ki te 2.

$$x=-\sqrt{17}-4$$

Kua oti te whārite te whakatau.

$$x=\sqrt{17}-4 x=-\sqrt{17}-4$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te x^{2} ki ngā taha e rua.

$$8x+x^{2}=1$$

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.

$$x^{2}+8x=1$$

Whakawehea te 8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 4. Nā, tāpiria te pūrua o te 4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+8x+4^{2}=1+4^{2}$$

Pūrua 4.

$$x^{2}+8x+16=1+16$$

Tāpiri 1 ki te 16.

$$x^{2}+8x+16=17$$

Tauwehea x^{2}+8x+16. 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}.

$$\left(x+4\right)^{2}=17$$

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

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{17}$$

Whakarūnātia.

$$x+4=\sqrt{17} x+4=-\sqrt{17}$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$x=\sqrt{17}-4 x=-\sqrt{17}-4$$