Whakaoti i te 15.1+xdivx(12)=3x

$$15.1+x \div x(12)=3x$$

Whakaoti mō x

$$x = \frac{271}{30} = 9\frac{1}{30} \approx 9.033333333$$

Ngā Upane Whakamahi Tauwehe

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$x\times 15.1+x\times 12=3xx$$

Whakareatia te x ki te x, ka x^{2}.

$$x\times 15.1+x\times 12=3x^{2}$$

Pahekotia te x\times 15.1 me x\times 12, ka 27.1x.

$$27.1x=3x^{2}$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$27.1x-3x^{2}=0$$

Tauwehea te x.

$$x\left(27.1-3x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 27.1-3x=0.

$$x=0 x=\frac{271}{30}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{271}{30}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$x\times 15.1+x\times 12=3xx$$

Whakareatia te x ki te x, ka x^{2}.

$$x\times 15.1+x\times 12=3x^{2}$$

Pahekotia te x\times 15.1 me x\times 12, ka 27.1x.

$$27.1x=3x^{2}$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$27.1x-3x^{2}=0$$

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.

$$-3x^{2}+27.1x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -3 mō a, 27.1 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-27.1±\sqrt{27.1^{2}}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 27.1^{2}.

$$x=\frac{-27.1±\frac{271}{10}}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$x=\frac{-27.1±\frac{271}{10}}{-6}$$

Nā, me whakaoti te whārite x=\frac{-27.1±\frac{271}{10}}{-6} ina he tāpiri te ±. Tāpiri -27.1 ki te \frac{271}{10} 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.

$$x=\frac{0}{-6}$$

Whakawehe 0 ki te -6.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-27.1±\frac{271}{10}}{-6} ina he tango te ±. Tango \frac{271}{10} mai i -27.1 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.

$$x=-\frac{\frac{271}{5}}{-6}$$

Whakawehe -\frac{271}{5} ki te -6.

$$x=\frac{271}{30}$$

Kua oti te whārite te whakatau.

$$x=0 x=\frac{271}{30}$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{271}{30}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te x.

$$x\times 15.1+x\times 12=3xx$$

Whakareatia te x ki te x, ka x^{2}.

$$x\times 15.1+x\times 12=3x^{2}$$

Pahekotia te x\times 15.1 me x\times 12, ka 27.1x.

$$27.1x=3x^{2}$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$27.1x-3x^{2}=0$$

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.

$$-3x^{2}+27.1x=0$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3x^{2}+27.1x}{-3}=\frac{0}{-3}$$

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

$$x^{2}+\frac{27.1}{-3}x=\frac{0}{-3}$$

Whakawehe 27.1 ki te -3.

$$x^{2}-\frac{271}{30}x=\frac{0}{-3}$$

Whakawehe 0 ki te -3.

$$x^{2}-\frac{271}{30}x=0$$

Whakawehea te -\frac{271}{30}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{271}{60}. Nā, tāpiria te pūrua o te -\frac{271}{60} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{271}{30}x+\left(-\frac{271}{60}\right)^{2}=\left(-\frac{271}{60}\right)^{2}$$

Pūruatia -\frac{271}{60} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{271}{30}x+\frac{73441}{3600}=\frac{73441}{3600}$$

Tauwehea x^{2}-\frac{271}{30}x+\frac{73441}{3600}. 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}.

$$\left(x-\frac{271}{60}\right)^{2}=\frac{73441}{3600}$$

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

$$\sqrt{\left(x-\frac{271}{60}\right)^{2}}=\sqrt{\frac{73441}{3600}}$$

Whakarūnātia.

$$x-\frac{271}{60}=\frac{271}{60} x-\frac{271}{60}=-\frac{271}{60}$$

Me tāpiri \frac{271}{60} ki ngā taha e rua o te whārite.

$$x=\frac{271}{30} x=0$$

Tē taea kia ōrite te tāupe x ki 0.

$$x=\frac{271}{30}$$