Whakaoti i te 30x^2+2x-0.8=0

$$30 x ^ { 2 } + 2 x - 0.8 = 0$$

Whakaoti mō x

$$x=\frac{2}{15}\approx 0.133333333$$

$$x=-0.2$$

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.

$$30x^{2}+2x-0.8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 30 mō a, 2 mō b, me -0.8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\times 30\left(-0.8\right)}}{2\times 30}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\times 30\left(-0.8\right)}}{2\times 30}$$

Whakareatia -4 ki te 30.

$$x=\frac{-2±\sqrt{4-120\left(-0.8\right)}}{2\times 30}$$

Whakareatia -120 ki te -0.8.

$$x=\frac{-2±\sqrt{4+96}}{2\times 30}$$

Tāpiri 4 ki te 96.

$$x=\frac{-2±\sqrt{100}}{2\times 30}$$

Tuhia te pūtakerua o te 100.

$$x=\frac{-2±10}{2\times 30}$$

Whakareatia 2 ki te 30.

$$x=\frac{-2±10}{60}$$

Nā, me whakaoti te whārite x=\frac{-2±10}{60} ina he tāpiri te ±. Tāpiri -2 ki te 10.

$$x=\frac{8}{60}$$

Whakahekea te hautanga \frac{8}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{2}{15}$$

Nā, me whakaoti te whārite x=\frac{-2±10}{60} ina he tango te ±. Tango 10 mai i -2.

$$x=-\frac{12}{60}$$

Whakahekea te hautanga \frac{-12}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

$$x=-\frac{1}{5}$$

Kua oti te whārite te whakatau.

$$x=\frac{2}{15} x=-\frac{1}{5}$$

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.

$$30x^{2}+2x-0.8=0$$

Me tāpiri 0.8 ki ngā taha e rua o te whārite.

$$30x^{2}+2x-0.8-\left(-0.8\right)=-\left(-0.8\right)$$

Mā te tango i te -0.8 i a ia ake anō ka toe ko te 0.

$$30x^{2}+2x=-\left(-0.8\right)$$

Tango -0.8 mai i 0.

$$30x^{2}+2x=0.8$$

Whakawehea ngā taha e rua ki te 30.

$$\frac{30x^{2}+2x}{30}=\frac{0.8}{30}$$

Mā te whakawehe ki te 30 ka wetekia te whakareanga ki te 30.

$$x^{2}+\frac{2}{30}x=\frac{0.8}{30}$$

Whakahekea te hautanga \frac{2}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}+\frac{1}{15}x=\frac{0.8}{30}$$

Whakawehe 0.8 ki te 30.

$$x^{2}+\frac{1}{15}x=\frac{2}{75}$$

Whakawehea te \frac{1}{15}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{30}. Nā, tāpiria te pūrua o te \frac{1}{30} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{1}{15}x+\left(\frac{1}{30}\right)^{2}=\frac{2}{75}+\left(\frac{1}{30}\right)^{2}$$

Pūruatia \frac{1}{30} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{1}{15}x+\frac{1}{900}=\frac{2}{75}+\frac{1}{900}$$

Tāpiri \frac{2}{75} ki te \frac{1}{900} 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.

$$x^{2}+\frac{1}{15}x+\frac{1}{900}=\frac{1}{36}$$

Tauwehea x^{2}+\frac{1}{15}x+\frac{1}{900}. 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}.

$$\left(x+\frac{1}{30}\right)^{2}=\frac{1}{36}$$

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

$$\sqrt{\left(x+\frac{1}{30}\right)^{2}}=\sqrt{\frac{1}{36}}$$

Whakarūnātia.

$$x+\frac{1}{30}=\frac{1}{6} x+\frac{1}{30}=-\frac{1}{6}$$

Me tango \frac{1}{30} mai i ngā taha e rua o te whārite.

$$x=\frac{2}{15} x=-\frac{1}{5}$$