Whakaoti i te left(3xright)^2+17x+10=0

$${ \left(3x \right) }^{ 2 } +17x+10=0$$

Whakaoti mō x (complex solution)

$$x=\frac{-17+\sqrt{71}i}{18}\approx -0.944444444+0.468119432i$$

$$x=\frac{-\sqrt{71}i-17}{18}\approx -0.944444444-0.468119432i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakarohaina te \left(3x\right)^{2}.

$$3^{2}x^{2}+17x+10=0$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$9x^{2}+17x+10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, 17 mō b, me 10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-17±\sqrt{17^{2}-4\times 9\times 10}}{2\times 9}$$

Pūrua 17.

$$x=\frac{-17±\sqrt{289-4\times 9\times 10}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{-17±\sqrt{289-36\times 10}}{2\times 9}$$

Whakareatia -36 ki te 10.

$$x=\frac{-17±\sqrt{289-360}}{2\times 9}$$

Tāpiri 289 ki te -360.

$$x=\frac{-17±\sqrt{-71}}{2\times 9}$$

Tuhia te pūtakerua o te -71.

$$x=\frac{-17±\sqrt{71}i}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{-17±\sqrt{71}i}{18}$$

Nā, me whakaoti te whārite x=\frac{-17±\sqrt{71}i}{18} ina he tāpiri te ±. Tāpiri -17 ki te i\sqrt{71}.

$$x=\frac{-17+\sqrt{71}i}{18}$$

Nā, me whakaoti te whārite x=\frac{-17±\sqrt{71}i}{18} ina he tango te ±. Tango i\sqrt{71} mai i -17.

$$x=\frac{-\sqrt{71}i-17}{18}$$

Kua oti te whārite te whakatau.

$$x=\frac{-17+\sqrt{71}i}{18} x=\frac{-\sqrt{71}i-17}{18}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakarohaina te \left(3x\right)^{2}.

$$3^{2}x^{2}+17x+10=0$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$9x^{2}+17x+10=0$$

Tangohia te 10 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$9x^{2}+17x=-10$$

Whakawehea ngā taha e rua ki te 9.

$$\frac{9x^{2}+17x}{9}=-\frac{10}{9}$$

Mā te whakawehe ki te 9 ka wetekia te whakareanga ki te 9.

$$x^{2}+\frac{17}{9}x=-\frac{10}{9}$$

Whakawehea te \frac{17}{9}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{17}{18}. Nā, tāpiria te pūrua o te \frac{17}{18} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{17}{9}x+\left(\frac{17}{18}\right)^{2}=-\frac{10}{9}+\left(\frac{17}{18}\right)^{2}$$

Pūruatia \frac{17}{18} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{17}{9}x+\frac{289}{324}=-\frac{10}{9}+\frac{289}{324}$$

Tāpiri -\frac{10}{9} ki te \frac{289}{324} 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.

$$x^{2}+\frac{17}{9}x+\frac{289}{324}=-\frac{71}{324}$$

Tauwehea x^{2}+\frac{17}{9}x+\frac{289}{324}. 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}.

$$\left(x+\frac{17}{18}\right)^{2}=-\frac{71}{324}$$

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

$$\sqrt{\left(x+\frac{17}{18}\right)^{2}}=\sqrt{-\frac{71}{324}}$$

Whakarūnātia.

$$x+\frac{17}{18}=\frac{\sqrt{71}i}{18} x+\frac{17}{18}=-\frac{\sqrt{71}i}{18}$$

Me tango \frac{17}{18} mai i ngā taha e rua o te whārite.

$$x=\frac{-17+\sqrt{71}i}{18} x=\frac{-\sqrt{71}i-17}{18}$$