Whakaoti i te 0.6x^2-0.2x+0.3=0

$$0.6 { x }^{ 2 } -0.2x+0.3 = 0$$

Whakaoti mō x (complex solution)

$$x=\frac{1+i\sqrt{17}}{6}\approx 0.166666667+0.687184271i$$

$$x=\frac{-i\sqrt{17}+1}{6}\approx 0.166666667-0.687184271i$$

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.

$$0.6x^{2}-0.2x+0.3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 0.6 mō a, -0.2 mō b, me 0.3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-0.2\right)±\sqrt{\left(-0.2\right)^{2}-4\times 0.6\times 0.3}}{2\times 0.6}$$

Pūruatia -0.2 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-0.2\right)±\sqrt{0.04-4\times 0.6\times 0.3}}{2\times 0.6}$$

Whakareatia -4 ki te 0.6.

$$x=\frac{-\left(-0.2\right)±\sqrt{0.04-2.4\times 0.3}}{2\times 0.6}$$

Whakareatia -2.4 ki te 0.3 mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{-\left(-0.2\right)±\sqrt{\frac{1-18}{25}}}{2\times 0.6}$$

Tāpiri 0.04 ki te -0.72 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.

$$x=\frac{-\left(-0.2\right)±\sqrt{-0.68}}{2\times 0.6}$$

Tuhia te pūtakerua o te -0.68.

$$x=\frac{-\left(-0.2\right)±\frac{\sqrt{17}i}{5}}{2\times 0.6}$$

Ko te tauaro o -0.2 ko 0.2.

$$x=\frac{0.2±\frac{\sqrt{17}i}{5}}{2\times 0.6}$$

Whakareatia 2 ki te 0.6.

$$x=\frac{0.2±\frac{\sqrt{17}i}{5}}{1.2}$$

Nā, me whakaoti te whārite x=\frac{0.2±\frac{\sqrt{17}i}{5}}{1.2} ina he tāpiri te ±. Tāpiri 0.2 ki te \frac{i\sqrt{17}}{5}.

$$x=\frac{1+\sqrt{17}i}{1.2\times 5}$$

Whakawehe \frac{1+i\sqrt{17}}{5} ki te 1.2 mā te whakarea \frac{1+i\sqrt{17}}{5} ki te tau huripoki o 1.2.

$$x=\frac{1+\sqrt{17}i}{6}$$

Nā, me whakaoti te whārite x=\frac{0.2±\frac{\sqrt{17}i}{5}}{1.2} ina he tango te ±. Tango \frac{i\sqrt{17}}{5} mai i 0.2.

$$x=\frac{-\sqrt{17}i+1}{1.2\times 5}$$

Whakawehe \frac{1-i\sqrt{17}}{5} ki te 1.2 mā te whakarea \frac{1-i\sqrt{17}}{5} ki te tau huripoki o 1.2.

$$x=\frac{-\sqrt{17}i+1}{6}$$

Kua oti te whārite te whakatau.

$$x=\frac{1+\sqrt{17}i}{6} x=\frac{-\sqrt{17}i+1}{6}$$

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.

$$0.6x^{2}-0.2x+0.3=0$$

Me tango 0.3 mai i ngā taha e rua o te whārite.

$$0.6x^{2}-0.2x+0.3-0.3=-0.3$$

Mā te tango i te 0.3 i a ia ake anō ka toe ko te 0.

$$0.6x^{2}-0.2x=-0.3$$

Whakawehea ngā taha e rua o te whārite ki te 0.6, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{0.6x^{2}-0.2x}{0.6}=-\frac{0.3}{0.6}$$

Mā te whakawehe ki te 0.6 ka wetekia te whakareanga ki te 0.6.

$$x^{2}+\left(-\frac{0.2}{0.6}\right)x=-\frac{0.3}{0.6}$$

Whakawehe -0.2 ki te 0.6 mā te whakarea -0.2 ki te tau huripoki o 0.6.

$$x^{2}-\frac{1}{3}x=-\frac{0.3}{0.6}$$

Whakawehe -0.3 ki te 0.6 mā te whakarea -0.3 ki te tau huripoki o 0.6.

$$x^{2}-\frac{1}{3}x=-0.5$$

Whakawehea te -\frac{1}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{6}. Nā, tāpiria te pūrua o te -\frac{1}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{3}x+\left(-\frac{1}{6}\right)^{2}=-0.5+\left(-\frac{1}{6}\right)^{2}$$

Pūruatia -\frac{1}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=-0.5+\frac{1}{36}$$

Tāpiri -0.5 ki te \frac{1}{36} 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.

$$x^{2}-\frac{1}{3}x+\frac{1}{36}=-\frac{17}{36}$$

Tauwehea x^{2}-\frac{1}{3}x+\frac{1}{36}. 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}.

$$\left(x-\frac{1}{6}\right)^{2}=-\frac{17}{36}$$

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

$$\sqrt{\left(x-\frac{1}{6}\right)^{2}}=\sqrt{-\frac{17}{36}}$$

Whakarūnātia.

$$x-\frac{1}{6}=\frac{\sqrt{17}i}{6} x-\frac{1}{6}=-\frac{\sqrt{17}i}{6}$$

Me tāpiri \frac{1}{6} ki ngā taha e rua o te whārite.

$$x=\frac{1+\sqrt{17}i}{6} x=\frac{-\sqrt{17}i+1}{6}$$