Whakaoti i te 20x^2+2x-0.8=0

$$20 x ^ { 2 } + 2 x - 0.8 = 0$$

Whakaoti mō x

$$x=\frac{\sqrt{17}-1}{20}\approx 0.156155281$$

$$x=\frac{-\sqrt{17}-1}{20}\approx -0.256155281$$

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.

$$20x^{2}+2x-0.8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 20 mō a, 2 mō b, me -0.8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\times 20\left(-0.8\right)}}{2\times 20}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\times 20\left(-0.8\right)}}{2\times 20}$$

Whakareatia -4 ki te 20.

$$x=\frac{-2±\sqrt{4-80\left(-0.8\right)}}{2\times 20}$$

Whakareatia -80 ki te -0.8.

$$x=\frac{-2±\sqrt{4+64}}{2\times 20}$$

Tāpiri 4 ki te 64.

$$x=\frac{-2±\sqrt{68}}{2\times 20}$$

Tuhia te pūtakerua o te 68.

$$x=\frac{-2±2\sqrt{17}}{2\times 20}$$

Whakareatia 2 ki te 20.

$$x=\frac{-2±2\sqrt{17}}{40}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{17}}{40} ina he tāpiri te ±. Tāpiri -2 ki te 2\sqrt{17}.

$$x=\frac{2\sqrt{17}-2}{40}$$

Whakawehe -2+2\sqrt{17} ki te 40.

$$x=\frac{\sqrt{17}-1}{20}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{17}}{40} ina he tango te ±. Tango 2\sqrt{17} mai i -2.

$$x=\frac{-2\sqrt{17}-2}{40}$$

Whakawehe -2-2\sqrt{17} ki te 40.

$$x=\frac{-\sqrt{17}-1}{20}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{17}-1}{20} x=\frac{-\sqrt{17}-1}{20}$$

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.

$$20x^{2}+2x-0.8=0$$

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

$$20x^{2}+2x-0.8-\left(-0.8\right)=-\left(-0.8\right)$$

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

$$20x^{2}+2x=-\left(-0.8\right)$$

Tango -0.8 mai i 0.

$$20x^{2}+2x=0.8$$

Whakawehea ngā taha e rua ki te 20.

$$\frac{20x^{2}+2x}{20}=\frac{0.8}{20}$$

Mā te whakawehe ki te 20 ka wetekia te whakareanga ki te 20.

$$x^{2}+\frac{2}{20}x=\frac{0.8}{20}$$

Whakahekea te hautanga \frac{2}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}+\frac{1}{10}x=\frac{0.8}{20}$$

Whakawehe 0.8 ki te 20.

$$x^{2}+\frac{1}{10}x=0.04$$

Whakawehea te \frac{1}{10}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{20}. Nā, tāpiria te pūrua o te \frac{1}{20} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{1}{10}x+\left(\frac{1}{20}\right)^{2}=0.04+\left(\frac{1}{20}\right)^{2}$$

Pūruatia \frac{1}{20} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{1}{10}x+\frac{1}{400}=0.04+\frac{1}{400}$$

Tāpiri 0.04 ki te \frac{1}{400} 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.

$$x^{2}+\frac{1}{10}x+\frac{1}{400}=\frac{17}{400}$$

Tauwehea x^{2}+\frac{1}{10}x+\frac{1}{400}. 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}.

$$\left(x+\frac{1}{20}\right)^{2}=\frac{17}{400}$$

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

$$\sqrt{\left(x+\frac{1}{20}\right)^{2}}=\sqrt{\frac{17}{400}}$$

Whakarūnātia.

$$x+\frac{1}{20}=\frac{\sqrt{17}}{20} x+\frac{1}{20}=-\frac{\sqrt{17}}{20}$$

Me tango \frac{1}{20} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{17}-1}{20} x=\frac{-\sqrt{17}-1}{20}$$