Whakaoti i te 3x^2+2.5x=12.5

$$3 x ^ { 2 } + 2.5 x = 12.5$$

Whakaoti mō x

$$x=-2.5$$

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

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.

$$3x^{2}+2.5x=12.5$$

Me tango 12.5 mai i ngā taha e rua o te whārite.

$$3x^{2}+2.5x-12.5=12.5-12.5$$

Mā te tango i te 12.5 i a ia ake anō ka toe ko te 0.

$$3x^{2}+2.5x-12.5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 2.5 mō b, me -12.5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2.5±\sqrt{2.5^{2}-4\times 3\left(-12.5\right)}}{2\times 3}$$

Pūruatia 2.5 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-2.5±\sqrt{6.25-4\times 3\left(-12.5\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-2.5±\sqrt{6.25-12\left(-12.5\right)}}{2\times 3}$$

Whakareatia -12 ki te -12.5.

$$x=\frac{-2.5±\sqrt{6.25+150}}{2\times 3}$$

Tāpiri 6.25 ki te 150.

$$x=\frac{-2.5±\sqrt{156.25}}{2\times 3}$$

Tuhia te pūtakerua o te 156.25.

$$x=\frac{-2.5±\frac{25}{2}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-2.5±\frac{25}{2}}{6}$$

Nā, me whakaoti te whārite x=\frac{-2.5±\frac{25}{2}}{6} ina he tāpiri te ±. Tāpiri -2.5 ki te \frac{25}{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.

$$x=\frac{10}{6}$$

Whakahekea te hautanga \frac{10}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{5}{3}$$

Nā, me whakaoti te whārite x=\frac{-2.5±\frac{25}{2}}{6} ina he tango te ±. Tango \frac{25}{2} mai i -2.5 mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=-\frac{15}{6}$$

Whakahekea te hautanga \frac{-15}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

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

Kua oti te whārite te whakatau.

$$x=\frac{5}{3} x=-\frac{5}{2}$$

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.

$$3x^{2}+2.5x=12.5$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}+2.5x}{3}=\frac{12.5}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$x^{2}+\frac{2.5}{3}x=\frac{12.5}{3}$$

Whakawehe 2.5 ki te 3.

$$x^{2}+\frac{5}{6}x=\frac{12.5}{3}$$

Whakawehe 12.5 ki te 3.

$$x^{2}+\frac{5}{6}x=\frac{25}{6}$$

Whakawehea te \frac{5}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{12}. Nā, tāpiria te pūrua o te \frac{5}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{5}{6}x+\frac{5}{12}^{2}=\frac{25}{6}+\frac{5}{12}^{2}$$

Pūruatia \frac{5}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{5}{6}x+\frac{25}{144}=\frac{25}{6}+\frac{25}{144}$$

Tāpiri \frac{25}{6} ki te \frac{25}{144} 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.

$$x^{2}+\frac{5}{6}x+\frac{25}{144}=\frac{625}{144}$$

Tauwehea x^{2}+\frac{5}{6}x+\frac{25}{144}. 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}.

$$\left(x+\frac{5}{12}\right)^{2}=\frac{625}{144}$$

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

$$\sqrt{\left(x+\frac{5}{12}\right)^{2}}=\sqrt{\frac{625}{144}}$$

Whakarūnātia.

$$x+\frac{5}{12}=\frac{25}{12} x+\frac{5}{12}=-\frac{25}{12}$$

Me tango \frac{5}{12} mai i ngā taha e rua o te whārite.

$$x=\frac{5}{3} x=-\frac{5}{2}$$