Whakaoti i te 18x-8=35x^2

$$18x-8=35 { x }^{ 2 }$$

Whakaoti mō x (complex solution)

$$x=\frac{-\sqrt{199}i+9}{35}\approx 0.257142857-0.403049599i$$

$$x=\frac{9+\sqrt{199}i}{35}\approx 0.257142857+0.403049599i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 35x^{2} mai i ngā taha e rua.

$$18x-8-35x^{2}=0$$

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.

$$-35x^{2}+18x-8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -35 mō a, 18 mō b, me -8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}-4\left(-35\right)\left(-8\right)}}{2\left(-35\right)}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\left(-35\right)\left(-8\right)}}{2\left(-35\right)}$$

Whakareatia -4 ki te -35.

$$x=\frac{-18±\sqrt{324+140\left(-8\right)}}{2\left(-35\right)}$$

Whakareatia 140 ki te -8.

$$x=\frac{-18±\sqrt{324-1120}}{2\left(-35\right)}$$

Tāpiri 324 ki te -1120.

$$x=\frac{-18±\sqrt{-796}}{2\left(-35\right)}$$

Tuhia te pūtakerua o te -796.

$$x=\frac{-18±2\sqrt{199}i}{2\left(-35\right)}$$

Whakareatia 2 ki te -35.

$$x=\frac{-18±2\sqrt{199}i}{-70}$$

Nā, me whakaoti te whārite x=\frac{-18±2\sqrt{199}i}{-70} ina he tāpiri te ±. Tāpiri -18 ki te 2i\sqrt{199}.

$$x=\frac{-18+2\sqrt{199}i}{-70}$$

Whakawehe -18+2i\sqrt{199} ki te -70.

$$x=\frac{-\sqrt{199}i+9}{35}$$

Nā, me whakaoti te whārite x=\frac{-18±2\sqrt{199}i}{-70} ina he tango te ±. Tango 2i\sqrt{199} mai i -18.

$$x=\frac{-2\sqrt{199}i-18}{-70}$$

Whakawehe -18-2i\sqrt{199} ki te -70.

$$x=\frac{9+\sqrt{199}i}{35}$$

Kua oti te whārite te whakatau.

$$x=\frac{-\sqrt{199}i+9}{35} x=\frac{9+\sqrt{199}i}{35}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 35x^{2} mai i ngā taha e rua.

$$18x-8-35x^{2}=0$$

Me tāpiri te 8 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$18x-35x^{2}=8$$

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.

$$-35x^{2}+18x=8$$

Whakawehea ngā taha e rua ki te -35.

$$\frac{-35x^{2}+18x}{-35}=\frac{8}{-35}$$

Mā te whakawehe ki te -35 ka wetekia te whakareanga ki te -35.

$$x^{2}+\frac{18}{-35}x=\frac{8}{-35}$$

Whakawehe 18 ki te -35.

$$x^{2}-\frac{18}{35}x=\frac{8}{-35}$$

Whakawehe 8 ki te -35.

$$x^{2}-\frac{18}{35}x=-\frac{8}{35}$$

Whakawehea te -\frac{18}{35}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{35}. Nā, tāpiria te pūrua o te -\frac{9}{35} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{18}{35}x+\left(-\frac{9}{35}\right)^{2}=-\frac{8}{35}+\left(-\frac{9}{35}\right)^{2}$$

Pūruatia -\frac{9}{35} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{18}{35}x+\frac{81}{1225}=-\frac{8}{35}+\frac{81}{1225}$$

Tāpiri -\frac{8}{35} ki te \frac{81}{1225} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{18}{35}x+\frac{81}{1225}=-\frac{199}{1225}$$

Tauwehea x^{2}-\frac{18}{35}x+\frac{81}{1225}. 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}.

$$\left(x-\frac{9}{35}\right)^{2}=-\frac{199}{1225}$$

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

$$\sqrt{\left(x-\frac{9}{35}\right)^{2}}=\sqrt{-\frac{199}{1225}}$$

Whakarūnātia.

$$x-\frac{9}{35}=\frac{\sqrt{199}i}{35} x-\frac{9}{35}=-\frac{\sqrt{199}i}{35}$$

Me tāpiri \frac{9}{35} ki ngā taha e rua o te whārite.

$$x=\frac{9+\sqrt{199}i}{35} x=\frac{-\sqrt{199}i+9}{35}$$