Whakaoti i te 0.8x^2+3.4x=1

$$0.8 x ^ { 2 } + 3.4 x = 1$$

Whakaoti mō x

$$x=\frac{3\sqrt{41}-17}{8}\approx 0.276171589$$

$$x=\frac{-3\sqrt{41}-17}{8}\approx -4.526171589$$

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.

$$0.8x^{2}+3.4x=1$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$0.8x^{2}+3.4x-1=1-1$$

Mā te tango i te 1 i a ia ake anō ka toe ko te 0.

$$0.8x^{2}+3.4x-1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 0.8 mō a, 3.4 mō b, me -1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-3.4±\sqrt{3.4^{2}-4\times 0.8\left(-1\right)}}{2\times 0.8}$$

Pūruatia 3.4 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-3.4±\sqrt{11.56-4\times 0.8\left(-1\right)}}{2\times 0.8}$$

Whakareatia -4 ki te 0.8.

$$x=\frac{-3.4±\sqrt{11.56-3.2\left(-1\right)}}{2\times 0.8}$$

Whakareatia -3.2 ki te -1.

$$x=\frac{-3.4±\sqrt{11.56+3.2}}{2\times 0.8}$$

Tāpiri 11.56 ki te 3.2 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.

$$x=\frac{-3.4±\sqrt{14.76}}{2\times 0.8}$$

Tuhia te pūtakerua o te 14.76.

$$x=\frac{-3.4±\frac{3\sqrt{41}}{5}}{2\times 0.8}$$

Whakareatia 2 ki te 0.8.

$$x=\frac{-3.4±\frac{3\sqrt{41}}{5}}{1.6}$$

Nā, me whakaoti te whārite x=\frac{-3.4±\frac{3\sqrt{41}}{5}}{1.6} ina he tāpiri te ±. Tāpiri -3.4 ki te \frac{3\sqrt{41}}{5}.

$$x=\frac{3\sqrt{41}-17}{1.6\times 5}$$

Whakawehe \frac{-17+3\sqrt{41}}{5} ki te 1.6 mā te whakarea \frac{-17+3\sqrt{41}}{5} ki te tau huripoki o 1.6.

$$x=\frac{3\sqrt{41}-17}{8}$$

Nā, me whakaoti te whārite x=\frac{-3.4±\frac{3\sqrt{41}}{5}}{1.6} ina he tango te ±. Tango \frac{3\sqrt{41}}{5} mai i -3.4.

$$x=\frac{-3\sqrt{41}-17}{1.6\times 5}$$

Whakawehe \frac{-17-3\sqrt{41}}{5} ki te 1.6 mā te whakarea \frac{-17-3\sqrt{41}}{5} ki te tau huripoki o 1.6.

$$x=\frac{-3\sqrt{41}-17}{8}$$

Kua oti te whārite te whakatau.

$$x=\frac{3\sqrt{41}-17}{8} x=\frac{-3\sqrt{41}-17}{8}$$

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.

$$0.8x^{2}+3.4x=1$$

Whakawehea ngā taha e rua o te whārite ki te 0.8, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

$$\frac{0.8x^{2}+3.4x}{0.8}=\frac{1}{0.8}$$

Mā te whakawehe ki te 0.8 ka wetekia te whakareanga ki te 0.8.

$$x^{2}+\frac{3.4}{0.8}x=\frac{1}{0.8}$$

Whakawehe 3.4 ki te 0.8 mā te whakarea 3.4 ki te tau huripoki o 0.8.

$$x^{2}+4.25x=\frac{1}{0.8}$$

Whakawehe 1 ki te 0.8 mā te whakarea 1 ki te tau huripoki o 0.8.

$$x^{2}+4.25x=1.25$$

Whakawehea te 4.25, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 2.125. Nā, tāpiria te pūrua o te 2.125 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+4.25x+2.125^{2}=1.25+2.125^{2}$$

Pūruatia 2.125 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+4.25x+4.515625=1.25+4.515625$$

Tāpiri 1.25 ki te 4.515625 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.

$$x^{2}+4.25x+4.515625=5.765625$$

Tauwehea te x^{2}+4.25x+4.515625. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+2.125\right)^{2}=5.765625$$

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

$$\sqrt{\left(x+2.125\right)^{2}}=\sqrt{5.765625}$$

Whakarūnātia.

$$x+2.125=\frac{3\sqrt{41}}{8} x+2.125=-\frac{3\sqrt{41}}{8}$$

Me tango 2.125 mai i ngā taha e rua o te whārite.

$$x=\frac{3\sqrt{41}-17}{8} x=\frac{-3\sqrt{41}-17}{8}$$