Whakaoti i te 1/4x-2x(x+6)=0

$$\frac{ 1 }{ 4 } x-2x(x+6)=0$$

Whakaoti mō x

$$x = -\frac{47}{8} = -5\frac{7}{8} = -5.875$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakareatia te -1 ki te 2, ka -2.

$$\frac{1}{4}x-2x\left(x+6\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2x ki te x+6.

$$\frac{1}{4}x-2x^{2}-12x=0$$

Pahekotia te \frac{1}{4}x me -12x, ka -\frac{47}{4}x.

$$-\frac{47}{4}x-2x^{2}=0$$

Tauwehea te x.

$$x\left(-\frac{47}{4}-2x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -\frac{47}{4}-2x=0.

$$x=0 x=-\frac{47}{8}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te -1 ki te 2, ka -2.

$$\frac{1}{4}x-2x\left(x+6\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2x ki te x+6.

$$\frac{1}{4}x-2x^{2}-12x=0$$

Pahekotia te \frac{1}{4}x me -12x, ka -\frac{47}{4}x.

$$-\frac{47}{4}x-2x^{2}=0$$

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.

$$-2x^{2}-\frac{47}{4}x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, -\frac{47}{4} mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{47}{4}\right)±\sqrt{\left(-\frac{47}{4}\right)^{2}}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te \left(-\frac{47}{4}\right)^{2}.

$$x=\frac{-\left(-\frac{47}{4}\right)±\frac{47}{4}}{2\left(-2\right)}$$

Ko te tauaro o -\frac{47}{4} ko \frac{47}{4}.

$$x=\frac{\frac{47}{4}±\frac{47}{4}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{\frac{47}{4}±\frac{47}{4}}{-4}$$

Nā, me whakaoti te whārite x=\frac{\frac{47}{4}±\frac{47}{4}}{-4} ina he tāpiri te ±. Tāpiri \frac{47}{4} ki te \frac{47}{4} 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.

$$x=\frac{\frac{47}{2}}{-4}$$

Whakawehe \frac{47}{2} ki te -4.

$$x=-\frac{47}{8}$$

Nā, me whakaoti te whārite x=\frac{\frac{47}{4}±\frac{47}{4}}{-4} ina he tango te ±. Tango \frac{47}{4} mai i \frac{47}{4} 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.

$$x=\frac{0}{-4}$$

Whakawehe 0 ki te -4.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-\frac{47}{8} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te -1 ki te 2, ka -2.

$$\frac{1}{4}x-2x\left(x+6\right)=0$$

Whakamahia te āhuatanga tohatoha hei whakarea te -2x ki te x+6.

$$\frac{1}{4}x-2x^{2}-12x=0$$

Pahekotia te \frac{1}{4}x me -12x, ka -\frac{47}{4}x.

$$-\frac{47}{4}x-2x^{2}=0$$

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.

$$-2x^{2}-\frac{47}{4}x=0$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2x^{2}-\frac{47}{4}x}{-2}=\frac{0}{-2}$$

Mā te whakawehe ki te -2 ka wetekia te whakareanga ki te -2.

$$x^{2}+\left(-\frac{\frac{47}{4}}{-2}\right)x=\frac{0}{-2}$$

Whakawehe -\frac{47}{4} ki te -2.

$$x^{2}+\frac{47}{8}x=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

$$x^{2}+\frac{47}{8}x=0$$

Whakawehea te \frac{47}{8}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{47}{16}. Nā, tāpiria te pūrua o te \frac{47}{16} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{47}{8}x+\left(\frac{47}{16}\right)^{2}=\left(\frac{47}{16}\right)^{2}$$

Pūruatia \frac{47}{16} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{47}{8}x+\frac{2209}{256}=\frac{2209}{256}$$

Tauwehea x^{2}+\frac{47}{8}x+\frac{2209}{256}. 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}.

$$\left(x+\frac{47}{16}\right)^{2}=\frac{2209}{256}$$

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

$$\sqrt{\left(x+\frac{47}{16}\right)^{2}}=\sqrt{\frac{2209}{256}}$$

Whakarūnātia.

$$x+\frac{47}{16}=\frac{47}{16} x+\frac{47}{16}=-\frac{47}{16}$$

Me tango \frac{47}{16} mai i ngā taha e rua o te whārite.

$$x=0 x=-\frac{47}{8}$$