Whakaoti i te x^2-25x+104=-7x-3

$$x ^ { 2 } - 25 x + 104 = - 7 x - 3$$

Whakaoti mō x (complex solution)

$$x=9+\sqrt{26}i\approx 9+5.099019514i$$

$$x=-\sqrt{26}i+9\approx 9-5.099019514i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 7x ki ngā taha e rua.

$$x^{2}-25x+104+7x=-3$$

Pahekotia te -25x me 7x, ka -18x.

$$x^{2}-18x+104=-3$$

Me tāpiri te 3 ki ngā taha e rua.

$$x^{2}-18x+104+3=0$$

Tāpirihia te 104 ki te 3, ka 107.

$$x^{2}-18x+107=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -18 mō b, me 107 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 107}}{2}$$

Pūrua -18.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 107}}{2}$$

Whakareatia -4 ki te 107.

$$x=\frac{-\left(-18\right)±\sqrt{324-428}}{2}$$

Tāpiri 324 ki te -428.

$$x=\frac{-\left(-18\right)±\sqrt{-104}}{2}$$

Tuhia te pūtakerua o te -104.

$$x=\frac{-\left(-18\right)±2\sqrt{26}i}{2}$$

Ko te tauaro o -18 ko 18.

$$x=\frac{18±2\sqrt{26}i}{2}$$

Nā, me whakaoti te whārite x=\frac{18±2\sqrt{26}i}{2} ina he tāpiri te ±. Tāpiri 18 ki te 2i\sqrt{26}.

$$x=\frac{18+2\sqrt{26}i}{2}$$

Whakawehe 18+2i\sqrt{26} ki te 2.

$$x=9+\sqrt{26}i$$

Nā, me whakaoti te whārite x=\frac{18±2\sqrt{26}i}{2} ina he tango te ±. Tango 2i\sqrt{26} mai i 18.

$$x=\frac{-2\sqrt{26}i+18}{2}$$

Whakawehe 18-2i\sqrt{26} ki te 2.

$$x=-\sqrt{26}i+9$$

Kua oti te whārite te whakatau.

$$x=9+\sqrt{26}i x=-\sqrt{26}i+9$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 7x ki ngā taha e rua.

$$x^{2}-25x+104+7x=-3$$

Pahekotia te -25x me 7x, ka -18x.

$$x^{2}-18x+104=-3$$

Tangohia te 104 mai i ngā taha e rua.

$$x^{2}-18x=-3-104$$

Tangohia te 104 i te -3, ka -107.

$$x^{2}-18x=-107$$

Whakawehea te -18, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -9. Nā, tāpiria te pūrua o te -9 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-18x+\left(-9\right)^{2}=-107+\left(-9\right)^{2}$$

Pūrua -9.

$$x^{2}-18x+81=-107+81$$

Tāpiri -107 ki te 81.

$$x^{2}-18x+81=-26$$

Tauwehea te x^{2}-18x+81. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-9\right)^{2}=-26$$

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

$$\sqrt{\left(x-9\right)^{2}}=\sqrt{-26}$$

Whakarūnātia.

$$x-9=\sqrt{26}i x-9=-\sqrt{26}i$$

Me tāpiri 9 ki ngā taha e rua o te whārite.

$$x=9+\sqrt{26}i x=-\sqrt{26}i+9$$