Whakaoti i te x^2+2x+358=29

$${ x }^{ 2 } +2x+358=29$$

Whakaoti mō x (complex solution)

$$x=-1+2\sqrt{82}i\approx -1+18.110770276i$$

$$x=-2\sqrt{82}i-1\approx -1-18.110770276i$$

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.

$$x^{2}+2x+358=29$$

Me tango 29 mai i ngā taha e rua o te whārite.

$$x^{2}+2x+358-29=29-29$$

Mā te tango i te 29 i a ia ake anō ka toe ko te 0.

$$x^{2}+2x+358-29=0$$

Tango 29 mai i 358.

$$x^{2}+2x+329=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me 329 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\times 329}}{2}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\times 329}}{2}$$

Whakareatia -4 ki te 329.

$$x=\frac{-2±\sqrt{4-1316}}{2}$$

Tāpiri 4 ki te -1316.

$$x=\frac{-2±\sqrt{-1312}}{2}$$

Tuhia te pūtakerua o te -1312.

$$x=\frac{-2±4\sqrt{82}i}{2}$$

Nā, me whakaoti te whārite x=\frac{-2±4\sqrt{82}i}{2} ina he tāpiri te ±. Tāpiri -2 ki te 4i\sqrt{82}.

$$x=\frac{-2+4\sqrt{82}i}{2}$$

Whakawehe -2+4i\sqrt{82} ki te 2.

$$x=-1+2\sqrt{82}i$$

Nā, me whakaoti te whārite x=\frac{-2±4\sqrt{82}i}{2} ina he tango te ±. Tango 4i\sqrt{82} mai i -2.

$$x=\frac{-4\sqrt{82}i-2}{2}$$

Whakawehe -2-4i\sqrt{82} ki te 2.

$$x=-2\sqrt{82}i-1$$

Kua oti te whārite te whakatau.

$$x=-1+2\sqrt{82}i x=-2\sqrt{82}i-1$$

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.

$$x^{2}+2x+358=29$$

Me tango 358 mai i ngā taha e rua o te whārite.

$$x^{2}+2x+358-358=29-358$$

Mā te tango i te 358 i a ia ake anō ka toe ko te 0.

$$x^{2}+2x=29-358$$

Tango 358 mai i 29.

$$x^{2}+2x=-329$$

Whakawehea te 2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1. Nā, tāpiria te pūrua o te 1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+2x+1^{2}=-329+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=-329+1$$

Tāpiri -329 ki te 1.

$$x^{2}+2x+1=-328$$

Tauwehea x^{2}+2x+1. 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}.

$$\left(x+1\right)^{2}=-328$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{-328}$$

Whakarūnātia.

$$x+1=2\sqrt{82}i x+1=-2\sqrt{82}i$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=-1+2\sqrt{82}i x=-2\sqrt{82}i-1$$