Whakaoti i te x^2+134=-2x-14

$${ x }^{ 2 } +134=-2x-14$$

Whakaoti mō x (complex solution)

$$x=-1+7\sqrt{3}i\approx -1+12.124355653i$$

$$x=-7\sqrt{3}i-1\approx -1-12.124355653i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 2x ki ngā taha e rua.

$$x^{2}+134+2x=-14$$

Me tāpiri te 14 ki ngā taha e rua.

$$x^{2}+134+2x+14=0$$

Tāpirihia te 134 ki te 14, ka 148.

$$x^{2}+148+2x=0$$

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.

$$x^{2}+2x+148=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 2 mō b, me 148 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\times 148}}{2}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\times 148}}{2}$$

Whakareatia -4 ki te 148.

$$x=\frac{-2±\sqrt{4-592}}{2}$$

Tāpiri 4 ki te -592.

$$x=\frac{-2±\sqrt{-588}}{2}$$

Tuhia te pūtakerua o te -588.

$$x=\frac{-2±14\sqrt{3}i}{2}$$

Nā, me whakaoti te whārite x=\frac{-2±14\sqrt{3}i}{2} ina he tāpiri te ±. Tāpiri -2 ki te 14i\sqrt{3}.

$$x=\frac{-2+14\sqrt{3}i}{2}$$

Whakawehe -2+14i\sqrt{3} ki te 2.

$$x=-1+7\sqrt{3}i$$

Nā, me whakaoti te whārite x=\frac{-2±14\sqrt{3}i}{2} ina he tango te ±. Tango 14i\sqrt{3} mai i -2.

$$x=\frac{-14\sqrt{3}i-2}{2}$$

Whakawehe -2-14i\sqrt{3} ki te 2.

$$x=-7\sqrt{3}i-1$$

Kua oti te whārite te whakatau.

$$x=-1+7\sqrt{3}i x=-7\sqrt{3}i-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 2x ki ngā taha e rua.

$$x^{2}+134+2x=-14$$

Tangohia te 134 mai i ngā taha e rua.

$$x^{2}+2x=-14-134$$

Tangohia te 134 i te -14, ka -148.

$$x^{2}+2x=-148$$

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.

$$x^{2}+2x+1^{2}=-148+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=-148+1$$

Tāpiri -148 ki te 1.

$$x^{2}+2x+1=-147$$

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}.

$$\left(x+1\right)^{2}=-147$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{-147}$$

Whakarūnātia.

$$x+1=7\sqrt{3}i x+1=-7\sqrt{3}i$$

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

$$x=-1+7\sqrt{3}i x=-7\sqrt{3}i-1$$