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

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

Whakaoti mō x (complex solution)

$$x=\frac{1+i\sqrt{7}}{4}\approx 0.25+0.661437828i$$

$$x=\frac{-i\sqrt{7}+1}{4}\approx 0.25-0.661437828i$$

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.

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

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

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

Pūruatia -0.3 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-0.3\right)±\sqrt{0.09-4\times 0.6\times 0.3}}{2\times 0.6}$$

Whakareatia -4 ki te 0.6.

$$x=\frac{-\left(-0.3\right)±\sqrt{0.09-2.4\times 0.3}}{2\times 0.6}$$

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.

$$x=\frac{-\left(-0.3\right)±\sqrt{0.09-0.72}}{2\times 0.6}$$

Tāpiri 0.09 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.

$$x=\frac{-\left(-0.3\right)±\sqrt{-0.63}}{2\times 0.6}$$

Tuhia te pūtakerua o te -0.63.

$$x=\frac{-\left(-0.3\right)±\frac{3\sqrt{7}i}{10}}{2\times 0.6}$$

Ko te tauaro o -0.3 ko 0.3.

$$x=\frac{0.3±\frac{3\sqrt{7}i}{10}}{2\times 0.6}$$

Whakareatia 2 ki te 0.6.

$$x=\frac{0.3±\frac{3\sqrt{7}i}{10}}{1.2}$$

Nā, me whakaoti te whārite x=\frac{0.3±\frac{3\sqrt{7}i}{10}}{1.2} ina he tāpiri te ±. Tāpiri 0.3 ki te \frac{3i\sqrt{7}}{10}.

$$x=\frac{3+3\sqrt{7}i}{1.2\times 10}$$

Whakawehe \frac{3+3i\sqrt{7}}{10} ki te 1.2 mā te whakarea \frac{3+3i\sqrt{7}}{10} ki te tau huripoki o 1.2.

$$x=\frac{1+\sqrt{7}i}{4}$$

Nā, me whakaoti te whārite x=\frac{0.3±\frac{3\sqrt{7}i}{10}}{1.2} ina he tango te ±. Tango \frac{3i\sqrt{7}}{10} mai i 0.3.

$$x=\frac{-3\sqrt{7}i+3}{1.2\times 10}$$

Whakawehe \frac{3-3i\sqrt{7}}{10} ki te 1.2 mā te whakarea \frac{3-3i\sqrt{7}}{10} ki te tau huripoki o 1.2.

$$x=\frac{-\sqrt{7}i+1}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{1+\sqrt{7}i}{4} x=\frac{-\sqrt{7}i+1}{4}$$

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.

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

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

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

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

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

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.

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

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

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

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

$$x^{2}-0.5x=-\frac{0.3}{0.6}$$

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

$$x^{2}-0.5x=-0.5$$

Whakawehea te -0.5, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -0.25. Nā, tāpiria te pūrua o te -0.25 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-0.5x+\left(-0.25\right)^{2}=-0.5+\left(-0.25\right)^{2}$$

Pūruatia -0.25 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-0.5x+0.0625=-0.5+0.0625$$

Tāpiri -0.5 ki te 0.0625 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.

$$x^{2}-0.5x+0.0625=-0.4375$$

Tauwehea x^{2}-0.5x+0.0625. 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}.

$$\left(x-0.25\right)^{2}=-0.4375$$

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

$$\sqrt{\left(x-0.25\right)^{2}}=\sqrt{-0.4375}$$

Whakarūnātia.

$$x-0.25=\frac{\sqrt{7}i}{4} x-0.25=-\frac{\sqrt{7}i}{4}$$

Me tāpiri 0.25 ki ngā taha e rua o te whārite.

$$x=\frac{1+\sqrt{7}i}{4} x=\frac{-\sqrt{7}i+1}{4}$$