Whakaoti i te -6/x=-x+5

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

Whakaoti mō x

$$x=-1$$

$$x=6$$

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.

$$-6=-xx+x\times 5$$

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

$$-6=-x^{2}+x\times 5$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-x^{2}+x\times 5=-6$$

Me tāpiri te 6 ki ngā taha e rua.

$$-x^{2}+x\times 5+6=0$$

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.

$$-x^{2}+5x+6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 5 mō b, me 6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-1\right)\times 6}}{2\left(-1\right)}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\left(-1\right)\times 6}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-5±\sqrt{25+4\times 6}}{2\left(-1\right)}$$

Whakareatia 4 ki te 6.

$$x=\frac{-5±\sqrt{25+24}}{2\left(-1\right)}$$

Tāpiri 25 ki te 24.

$$x=\frac{-5±\sqrt{49}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 49.

$$x=\frac{-5±7}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-5±7}{-2}$$

Nā, me whakaoti te whārite x=\frac{-5±7}{-2} ina he tāpiri te ±. Tāpiri -5 ki te 7.

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

Whakawehe 2 ki te -2.

$$x=-1$$

Nā, me whakaoti te whārite x=\frac{-5±7}{-2} ina he tango te ±. Tango 7 mai i -5.

$$x=-\frac{12}{-2}$$

Whakawehe -12 ki te -2.

$$x=6$$

Kua oti te whārite te whakatau.

$$x=-1 x=6$$

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.

$$-6=-xx+x\times 5$$

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

$$-6=-x^{2}+x\times 5$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$-x^{2}+x\times 5=-6$$

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.

$$-x^{2}+5x=-6$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+5x}{-1}=-\frac{6}{-1}$$

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

$$x^{2}+\frac{5}{-1}x=-\frac{6}{-1}$$

Whakawehe 5 ki te -1.

$$x^{2}-5x=-\frac{6}{-1}$$

Whakawehe -6 ki te -1.

$$x^{2}-5x=6$$

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

$$x^{2}-5x+\left(-\frac{5}{2}\right)^{2}=6+\left(-\frac{5}{2}\right)^{2}$$

Pūruatia -\frac{5}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-5x+\frac{25}{4}=6+\frac{25}{4}$$

Tāpiri 6 ki te \frac{25}{4}.

$$x^{2}-5x+\frac{25}{4}=\frac{49}{4}$$

Tauwehea x^{2}-5x+\frac{25}{4}. 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}.

$$\left(x-\frac{5}{2}\right)^{2}=\frac{49}{4}$$

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

$$\sqrt{\left(x-\frac{5}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Whakarūnātia.

$$x-\frac{5}{2}=\frac{7}{2} x-\frac{5}{2}=-\frac{7}{2}$$

Me tāpiri \frac{5}{2} ki ngā taha e rua o te whārite.

$$x=6 x=-1$$