Whakaoti i te -x*(x-8.1)=0

$$- x \cdot ( x - 8.1 ) = 0$$

Whakaoti mō x

$$x=8.1$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te -x ki te x-8.1.

$$\left(-x\right)x-8.1\left(-x\right)=0$$

Whakareatia te -8.1 ki te -1, ka 8.1.

$$\left(-x\right)x+8.1x=0$$

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

$$-x^{2}+8.1x=0$$

Tauwehea te x.

$$x\left(-x+8.1\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -x+8.1=0.

$$x=0 x=\frac{81}{10}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te -x ki te x-8.1.

$$\left(-x\right)x-8.1\left(-x\right)=0$$

Whakareatia te -8.1 ki te -1, ka 8.1.

$$\left(-x\right)x+8.1x=0$$

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

$$-x^{2}+8.1x=0$$

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.

$$-x^{2}+\frac{81}{10}x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, \frac{81}{10} mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\frac{81}{10}±\sqrt{\left(\frac{81}{10}\right)^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te \left(\frac{81}{10}\right)^{2}.

$$x=\frac{-\frac{81}{10}±\frac{81}{10}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-\frac{81}{10}±\frac{81}{10}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-\frac{81}{10}±\frac{81}{10}}{-2} ina he tāpiri te ±. Tāpiri -\frac{81}{10} ki te \frac{81}{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.

$$x=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-\frac{81}{10}±\frac{81}{10}}{-2} ina he tango te ±. Tango \frac{81}{10} mai i -\frac{81}{10} 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.

$$x=-\frac{\frac{81}{5}}{-2}$$

Whakawehe -\frac{81}{5} ki te -2.

$$x=\frac{81}{10}$$

Kua oti te whārite te whakatau.

$$x=0 x=\frac{81}{10}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te -x ki te x-8.1.

$$\left(-x\right)x-8.1\left(-x\right)=0$$

Whakareatia te -8.1 ki te -1, ka 8.1.

$$\left(-x\right)x+8.1x=0$$

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

$$-x^{2}+8.1x=0$$

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.

$$-x^{2}+\frac{81}{10}x=0$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+\frac{81}{10}x}{-1}=\frac{0}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{\frac{81}{10}}{-1}x=\frac{0}{-1}$$

Whakawehe \frac{81}{10} ki te -1.

$$x^{2}-\frac{81}{10}x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$x^{2}-\frac{81}{10}x=0$$

Whakawehea te -\frac{81}{10}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{81}{20}. Nā, tāpiria te pūrua o te -\frac{81}{20} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{81}{10}x+\left(-\frac{81}{20}\right)^{2}=\left(-\frac{81}{20}\right)^{2}$$

Pūruatia -\frac{81}{20} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{81}{10}x+\frac{6561}{400}=\frac{6561}{400}$$

Tauwehea x^{2}-\frac{81}{10}x+\frac{6561}{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}.

$$\left(x-\frac{81}{20}\right)^{2}=\frac{6561}{400}$$

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

$$\sqrt{\left(x-\frac{81}{20}\right)^{2}}=\sqrt{\frac{6561}{400}}$$

Whakarūnātia.

$$x-\frac{81}{20}=\frac{81}{20} x-\frac{81}{20}=-\frac{81}{20}$$

Me tāpiri \frac{81}{20} ki ngā taha e rua o te whārite.

$$x=\frac{81}{10} x=0$$