Whakaoti i te (3-6x)-17=(4-3x)*(5-4x)-2

$$( 3 - 6 x ) - 17 = ( 4 - 3 x ) \cdot ( 5 - 4 x ) - 2$$

Whakaoti mō x (complex solution)

$$x=\frac{25+\sqrt{911}i}{24}\approx 1.041666667+1.257615689i$$

$$x=\frac{-\sqrt{911}i+25}{24}\approx 1.041666667-1.257615689i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 17 i te 3, ka -14.

$$-14-6x=\left(4-3x\right)\left(5-4x\right)-2$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4-3x ki te 5-4x ka whakakotahi i ngā kupu rite.

$$-14-6x=20-31x+12x^{2}-2$$

Tangohia te 2 i te 20, ka 18.

$$-14-6x=18-31x+12x^{2}$$

Tangohia te 18 mai i ngā taha e rua.

$$-14-6x-18=-31x+12x^{2}$$

Tangohia te 18 i te -14, ka -32.

$$-32-6x=-31x+12x^{2}$$

Me tāpiri te 31x ki ngā taha e rua.

$$-32-6x+31x=12x^{2}$$

Pahekotia te -6x me 31x, ka 25x.

$$-32+25x=12x^{2}$$

Tangohia te 12x^{2} mai i ngā taha e rua.

$$-32+25x-12x^{2}=0$$

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.

$$-12x^{2}+25x-32=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -12 mō a, 25 mō b, me -32 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-25±\sqrt{25^{2}-4\left(-12\right)\left(-32\right)}}{2\left(-12\right)}$$

Pūrua 25.

$$x=\frac{-25±\sqrt{625-4\left(-12\right)\left(-32\right)}}{2\left(-12\right)}$$

Whakareatia -4 ki te -12.

$$x=\frac{-25±\sqrt{625+48\left(-32\right)}}{2\left(-12\right)}$$

Whakareatia 48 ki te -32.

$$x=\frac{-25±\sqrt{625-1536}}{2\left(-12\right)}$$

Tāpiri 625 ki te -1536.

$$x=\frac{-25±\sqrt{-911}}{2\left(-12\right)}$$

Tuhia te pūtakerua o te -911.

$$x=\frac{-25±\sqrt{911}i}{2\left(-12\right)}$$

Whakareatia 2 ki te -12.

$$x=\frac{-25±\sqrt{911}i}{-24}$$

Nā, me whakaoti te whārite x=\frac{-25±\sqrt{911}i}{-24} ina he tāpiri te ±. Tāpiri -25 ki te i\sqrt{911}.

$$x=\frac{-25+\sqrt{911}i}{-24}$$

Whakawehe -25+i\sqrt{911} ki te -24.

$$x=\frac{-\sqrt{911}i+25}{24}$$

Nā, me whakaoti te whārite x=\frac{-25±\sqrt{911}i}{-24} ina he tango te ±. Tango i\sqrt{911} mai i -25.

$$x=\frac{-\sqrt{911}i-25}{-24}$$

Whakawehe -25-i\sqrt{911} ki te -24.

$$x=\frac{25+\sqrt{911}i}{24}$$

Kua oti te whārite te whakatau.

$$x=\frac{-\sqrt{911}i+25}{24} x=\frac{25+\sqrt{911}i}{24}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 17 i te 3, ka -14.

$$-14-6x=\left(4-3x\right)\left(5-4x\right)-2$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 4-3x ki te 5-4x ka whakakotahi i ngā kupu rite.

$$-14-6x=20-31x+12x^{2}-2$$

Tangohia te 2 i te 20, ka 18.

$$-14-6x=18-31x+12x^{2}$$

Me tāpiri te 31x ki ngā taha e rua.

$$-14-6x+31x=18+12x^{2}$$

Pahekotia te -6x me 31x, ka 25x.

$$-14+25x=18+12x^{2}$$

Tangohia te 12x^{2} mai i ngā taha e rua.

$$-14+25x-12x^{2}=18$$

Me tāpiri te 14 ki ngā taha e rua.

$$25x-12x^{2}=18+14$$

Tāpirihia te 18 ki te 14, ka 32.

$$25x-12x^{2}=32$$

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.

$$-12x^{2}+25x=32$$

Whakawehea ngā taha e rua ki te -12.

$$\frac{-12x^{2}+25x}{-12}=\frac{32}{-12}$$

Mā te whakawehe ki te -12 ka wetekia te whakareanga ki te -12.

$$x^{2}+\frac{25}{-12}x=\frac{32}{-12}$$

Whakawehe 25 ki te -12.

$$x^{2}-\frac{25}{12}x=\frac{32}{-12}$$

Whakahekea te hautanga \frac{32}{-12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-\frac{25}{12}x=-\frac{8}{3}$$

Whakawehea te -\frac{25}{12}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{25}{24}. Nā, tāpiria te pūrua o te -\frac{25}{24} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{25}{12}x+\left(-\frac{25}{24}\right)^{2}=-\frac{8}{3}+\left(-\frac{25}{24}\right)^{2}$$

Pūruatia -\frac{25}{24} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{25}{12}x+\frac{625}{576}=-\frac{8}{3}+\frac{625}{576}$$

Tāpiri -\frac{8}{3} ki te \frac{625}{576} 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.

$$x^{2}-\frac{25}{12}x+\frac{625}{576}=-\frac{911}{576}$$

Tauwehea x^{2}-\frac{25}{12}x+\frac{625}{576}. 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}.

$$\left(x-\frac{25}{24}\right)^{2}=-\frac{911}{576}$$

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

$$\sqrt{\left(x-\frac{25}{24}\right)^{2}}=\sqrt{-\frac{911}{576}}$$

Whakarūnātia.

$$x-\frac{25}{24}=\frac{\sqrt{911}i}{24} x-\frac{25}{24}=-\frac{\sqrt{911}i}{24}$$

Me tāpiri \frac{25}{24} ki ngā taha e rua o te whārite.

$$x=\frac{25+\sqrt{911}i}{24} x=\frac{-\sqrt{911}i+25}{24}$$